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Magneto statics
AP Physics
Magnetism
1 Permanent Magnetsndash Objects that retain their magnetic propertiesbull Ex the magnet in a compass bar magnet horseshoe magnet
speakers and of course the magnets on the fridge
2 Electromagnetsndash Objects that exhibit magnetic properties as a result of
electric currentbull Ex electric motors
disk drives amp speakers
DWT
The properties of attraction possessed by magnets
MagnetsMagnets have two poleshellip
Similar to electric chargehellipopposites poles
Magnetic Fields (B) amp Forces1 A permanent magnet a moving charge or a current
creates a magnetic field B at all points in the surrounding space
2 The magnetic field exerts a force F on any other permanent magnet moving charge or current that is present in the field
Magnetic Dipole
Magnetic Field of Earth
Magnetic Forces IThe force acting on a moving charge in a B field is
1 proportional to the magnitude of the2 proportional to the magnitude of the3 proportional to the component of the
q
B
vθ
Right Hand Rule (RHR)DWTThe direction and the magnitude of the magnetic force is determined by a cross product computation (vector calculus ugh) Wersquoll cheat and use our hands (correction just right hand) rather than calculus
Right Hand Rule 11 Fingers in direction of B Field2 Thumb in direction of chargersquos
velocity v3a Positive Charge
Direction of Force corresponds to direction of the palm
3b Negative ChargeDirection of Force corresponds to direction of back of hand
RHR1 Examples
Notation used for Fieldsx ndash into surfacepage
(dot) ndash out of surfacepage
JJ Thomsonrsquos em RatioDWT Sir Joseph John ldquoJJrdquo Thomson (1856 ndash 1940) was a British physicist and Nobel laureate
credited for the discovery of the electron (Physics Nobel Prize in 1906) and the invention of the mass spectrometer
Thomson used a cathode ray tube to fire a stream of electrons through magnetic and electric fields (1897)
From his experiments he determined1 that there must be some small negatively charged particle (known today as
the electron JJ called them corpuscles)2 the charge to mass ratio (em ratio) of this new particle dubbed the electron
JJrsquos Cathode Ray Tube (simplified)
Actual Apparatus
Velocity Selector
Mass SpectrometerA scientific device that uses electric and
magnetic fields to determine the mass of a substance
How it Works1 Substance is ionized and vaporized2 Charged plates accelerate particles3 Particles pass through magnetic and
electric fields (velocity selector)4 Particles move in a curved path in the
presence of a magnetic field
Curved Motion Due to B FieldWhat is the radius R of the circular motion of the particle as
a result of the magnetic force
Mars RoverScientists want to include a compact mass
spectrometer on a future Mars rover Suppose the instrument is designed to have a magnetic field of 001 T and selects carbon ions that have a speed of 5 x 103 ms and are singly ionized (have a charge of +e) What are the radii R12 and R13 of the orbits of 12C and 13C ions in this spectrometer
A particle of mass m and charge ndashq is accelerated through a potential difference ε It then passes into a uniform magnetic field of magnitude B directed into the page as shown below Express your answers in terms of m q ε and B
a) Determine the speed of the electron as it enters the magnetic field
b) Sketch the path of the electron in the magnetic field on the diagram above
c) Determine the radius of the path of the electrond) An electric field E is now established in the same region
as the magnetic field so that the electron passes through the field undeflected
(i) Determine the magnitude of E(ii) Indicate the direction of E on the diagram above
Particle in Magnetic Field
Magnetic Forces IIThe force acting on a segment of conductor with length l
carrying a current I in a uniform B field is
B
θ I
l
Right Hand Rule Dos (RHR2)
Right Hand Rule 21 Fingers in direction of B Field2 Thumb in direction of
conductorrsquos current I(remember current is direction of positive charges)
3 Direction of Force corresponds to direction of the palm
B Force on Current LoopHow do the magnetic forces act on a current carrying loop
B Force on Current Loop Cont
Electric MotorsMotors operate because of the magnetic force on current carrying
conductors
Force on Conducting BarMagnetic forces are used to accelerate current carrying
conductors
B Fields From E CurrentsAn electric current creates a magnetic field
Simplest example Long straight wire
Right Hand Rule Trois (RHR3)
Right Hand Rule 31 Thumb in direction of
current2 Curl fingers in direction
of B field
Current Carrying Wire amp Compass
Force bw Parallel WiresHow do current carrying wires affect one another
SolenoidsAlmost like the magneto static equivalent of electrostaticsrsquo
parallel plate capacitor
Magnetism
1 Permanent Magnetsndash Objects that retain their magnetic propertiesbull Ex the magnet in a compass bar magnet horseshoe magnet
speakers and of course the magnets on the fridge
2 Electromagnetsndash Objects that exhibit magnetic properties as a result of
electric currentbull Ex electric motors
disk drives amp speakers
DWT
The properties of attraction possessed by magnets
MagnetsMagnets have two poleshellip
Similar to electric chargehellipopposites poles
Magnetic Fields (B) amp Forces1 A permanent magnet a moving charge or a current
creates a magnetic field B at all points in the surrounding space
2 The magnetic field exerts a force F on any other permanent magnet moving charge or current that is present in the field
Magnetic Dipole
Magnetic Field of Earth
Magnetic Forces IThe force acting on a moving charge in a B field is
1 proportional to the magnitude of the2 proportional to the magnitude of the3 proportional to the component of the
q
B
vθ
Right Hand Rule (RHR)DWTThe direction and the magnitude of the magnetic force is determined by a cross product computation (vector calculus ugh) Wersquoll cheat and use our hands (correction just right hand) rather than calculus
Right Hand Rule 11 Fingers in direction of B Field2 Thumb in direction of chargersquos
velocity v3a Positive Charge
Direction of Force corresponds to direction of the palm
3b Negative ChargeDirection of Force corresponds to direction of back of hand
RHR1 Examples
Notation used for Fieldsx ndash into surfacepage
(dot) ndash out of surfacepage
JJ Thomsonrsquos em RatioDWT Sir Joseph John ldquoJJrdquo Thomson (1856 ndash 1940) was a British physicist and Nobel laureate
credited for the discovery of the electron (Physics Nobel Prize in 1906) and the invention of the mass spectrometer
Thomson used a cathode ray tube to fire a stream of electrons through magnetic and electric fields (1897)
From his experiments he determined1 that there must be some small negatively charged particle (known today as
the electron JJ called them corpuscles)2 the charge to mass ratio (em ratio) of this new particle dubbed the electron
JJrsquos Cathode Ray Tube (simplified)
Actual Apparatus
Velocity Selector
Mass SpectrometerA scientific device that uses electric and
magnetic fields to determine the mass of a substance
How it Works1 Substance is ionized and vaporized2 Charged plates accelerate particles3 Particles pass through magnetic and
electric fields (velocity selector)4 Particles move in a curved path in the
presence of a magnetic field
Curved Motion Due to B FieldWhat is the radius R of the circular motion of the particle as
a result of the magnetic force
Mars RoverScientists want to include a compact mass
spectrometer on a future Mars rover Suppose the instrument is designed to have a magnetic field of 001 T and selects carbon ions that have a speed of 5 x 103 ms and are singly ionized (have a charge of +e) What are the radii R12 and R13 of the orbits of 12C and 13C ions in this spectrometer
A particle of mass m and charge ndashq is accelerated through a potential difference ε It then passes into a uniform magnetic field of magnitude B directed into the page as shown below Express your answers in terms of m q ε and B
a) Determine the speed of the electron as it enters the magnetic field
b) Sketch the path of the electron in the magnetic field on the diagram above
c) Determine the radius of the path of the electrond) An electric field E is now established in the same region
as the magnetic field so that the electron passes through the field undeflected
(i) Determine the magnitude of E(ii) Indicate the direction of E on the diagram above
Particle in Magnetic Field
Magnetic Forces IIThe force acting on a segment of conductor with length l
carrying a current I in a uniform B field is
B
θ I
l
Right Hand Rule Dos (RHR2)
Right Hand Rule 21 Fingers in direction of B Field2 Thumb in direction of
conductorrsquos current I(remember current is direction of positive charges)
3 Direction of Force corresponds to direction of the palm
B Force on Current LoopHow do the magnetic forces act on a current carrying loop
B Force on Current Loop Cont
Electric MotorsMotors operate because of the magnetic force on current carrying
conductors
Force on Conducting BarMagnetic forces are used to accelerate current carrying
conductors
B Fields From E CurrentsAn electric current creates a magnetic field
Simplest example Long straight wire
Right Hand Rule Trois (RHR3)
Right Hand Rule 31 Thumb in direction of
current2 Curl fingers in direction
of B field
Current Carrying Wire amp Compass
Force bw Parallel WiresHow do current carrying wires affect one another
SolenoidsAlmost like the magneto static equivalent of electrostaticsrsquo
parallel plate capacitor
MagnetsMagnets have two poleshellip
Similar to electric chargehellipopposites poles
Magnetic Fields (B) amp Forces1 A permanent magnet a moving charge or a current
creates a magnetic field B at all points in the surrounding space
2 The magnetic field exerts a force F on any other permanent magnet moving charge or current that is present in the field
Magnetic Dipole
Magnetic Field of Earth
Magnetic Forces IThe force acting on a moving charge in a B field is
1 proportional to the magnitude of the2 proportional to the magnitude of the3 proportional to the component of the
q
B
vθ
Right Hand Rule (RHR)DWTThe direction and the magnitude of the magnetic force is determined by a cross product computation (vector calculus ugh) Wersquoll cheat and use our hands (correction just right hand) rather than calculus
Right Hand Rule 11 Fingers in direction of B Field2 Thumb in direction of chargersquos
velocity v3a Positive Charge
Direction of Force corresponds to direction of the palm
3b Negative ChargeDirection of Force corresponds to direction of back of hand
RHR1 Examples
Notation used for Fieldsx ndash into surfacepage
(dot) ndash out of surfacepage
JJ Thomsonrsquos em RatioDWT Sir Joseph John ldquoJJrdquo Thomson (1856 ndash 1940) was a British physicist and Nobel laureate
credited for the discovery of the electron (Physics Nobel Prize in 1906) and the invention of the mass spectrometer
Thomson used a cathode ray tube to fire a stream of electrons through magnetic and electric fields (1897)
From his experiments he determined1 that there must be some small negatively charged particle (known today as
the electron JJ called them corpuscles)2 the charge to mass ratio (em ratio) of this new particle dubbed the electron
JJrsquos Cathode Ray Tube (simplified)
Actual Apparatus
Velocity Selector
Mass SpectrometerA scientific device that uses electric and
magnetic fields to determine the mass of a substance
How it Works1 Substance is ionized and vaporized2 Charged plates accelerate particles3 Particles pass through magnetic and
electric fields (velocity selector)4 Particles move in a curved path in the
presence of a magnetic field
Curved Motion Due to B FieldWhat is the radius R of the circular motion of the particle as
a result of the magnetic force
Mars RoverScientists want to include a compact mass
spectrometer on a future Mars rover Suppose the instrument is designed to have a magnetic field of 001 T and selects carbon ions that have a speed of 5 x 103 ms and are singly ionized (have a charge of +e) What are the radii R12 and R13 of the orbits of 12C and 13C ions in this spectrometer
A particle of mass m and charge ndashq is accelerated through a potential difference ε It then passes into a uniform magnetic field of magnitude B directed into the page as shown below Express your answers in terms of m q ε and B
a) Determine the speed of the electron as it enters the magnetic field
b) Sketch the path of the electron in the magnetic field on the diagram above
c) Determine the radius of the path of the electrond) An electric field E is now established in the same region
as the magnetic field so that the electron passes through the field undeflected
(i) Determine the magnitude of E(ii) Indicate the direction of E on the diagram above
Particle in Magnetic Field
Magnetic Forces IIThe force acting on a segment of conductor with length l
carrying a current I in a uniform B field is
B
θ I
l
Right Hand Rule Dos (RHR2)
Right Hand Rule 21 Fingers in direction of B Field2 Thumb in direction of
conductorrsquos current I(remember current is direction of positive charges)
3 Direction of Force corresponds to direction of the palm
B Force on Current LoopHow do the magnetic forces act on a current carrying loop
B Force on Current Loop Cont
Electric MotorsMotors operate because of the magnetic force on current carrying
conductors
Force on Conducting BarMagnetic forces are used to accelerate current carrying
conductors
B Fields From E CurrentsAn electric current creates a magnetic field
Simplest example Long straight wire
Right Hand Rule Trois (RHR3)
Right Hand Rule 31 Thumb in direction of
current2 Curl fingers in direction
of B field
Current Carrying Wire amp Compass
Force bw Parallel WiresHow do current carrying wires affect one another
SolenoidsAlmost like the magneto static equivalent of electrostaticsrsquo
parallel plate capacitor
Magnetic Fields (B) amp Forces1 A permanent magnet a moving charge or a current
creates a magnetic field B at all points in the surrounding space
2 The magnetic field exerts a force F on any other permanent magnet moving charge or current that is present in the field
Magnetic Dipole
Magnetic Field of Earth
Magnetic Forces IThe force acting on a moving charge in a B field is
1 proportional to the magnitude of the2 proportional to the magnitude of the3 proportional to the component of the
q
B
vθ
Right Hand Rule (RHR)DWTThe direction and the magnitude of the magnetic force is determined by a cross product computation (vector calculus ugh) Wersquoll cheat and use our hands (correction just right hand) rather than calculus
Right Hand Rule 11 Fingers in direction of B Field2 Thumb in direction of chargersquos
velocity v3a Positive Charge
Direction of Force corresponds to direction of the palm
3b Negative ChargeDirection of Force corresponds to direction of back of hand
RHR1 Examples
Notation used for Fieldsx ndash into surfacepage
(dot) ndash out of surfacepage
JJ Thomsonrsquos em RatioDWT Sir Joseph John ldquoJJrdquo Thomson (1856 ndash 1940) was a British physicist and Nobel laureate
credited for the discovery of the electron (Physics Nobel Prize in 1906) and the invention of the mass spectrometer
Thomson used a cathode ray tube to fire a stream of electrons through magnetic and electric fields (1897)
From his experiments he determined1 that there must be some small negatively charged particle (known today as
the electron JJ called them corpuscles)2 the charge to mass ratio (em ratio) of this new particle dubbed the electron
JJrsquos Cathode Ray Tube (simplified)
Actual Apparatus
Velocity Selector
Mass SpectrometerA scientific device that uses electric and
magnetic fields to determine the mass of a substance
How it Works1 Substance is ionized and vaporized2 Charged plates accelerate particles3 Particles pass through magnetic and
electric fields (velocity selector)4 Particles move in a curved path in the
presence of a magnetic field
Curved Motion Due to B FieldWhat is the radius R of the circular motion of the particle as
a result of the magnetic force
Mars RoverScientists want to include a compact mass
spectrometer on a future Mars rover Suppose the instrument is designed to have a magnetic field of 001 T and selects carbon ions that have a speed of 5 x 103 ms and are singly ionized (have a charge of +e) What are the radii R12 and R13 of the orbits of 12C and 13C ions in this spectrometer
A particle of mass m and charge ndashq is accelerated through a potential difference ε It then passes into a uniform magnetic field of magnitude B directed into the page as shown below Express your answers in terms of m q ε and B
a) Determine the speed of the electron as it enters the magnetic field
b) Sketch the path of the electron in the magnetic field on the diagram above
c) Determine the radius of the path of the electrond) An electric field E is now established in the same region
as the magnetic field so that the electron passes through the field undeflected
(i) Determine the magnitude of E(ii) Indicate the direction of E on the diagram above
Particle in Magnetic Field
Magnetic Forces IIThe force acting on a segment of conductor with length l
carrying a current I in a uniform B field is
B
θ I
l
Right Hand Rule Dos (RHR2)
Right Hand Rule 21 Fingers in direction of B Field2 Thumb in direction of
conductorrsquos current I(remember current is direction of positive charges)
3 Direction of Force corresponds to direction of the palm
B Force on Current LoopHow do the magnetic forces act on a current carrying loop
B Force on Current Loop Cont
Electric MotorsMotors operate because of the magnetic force on current carrying
conductors
Force on Conducting BarMagnetic forces are used to accelerate current carrying
conductors
B Fields From E CurrentsAn electric current creates a magnetic field
Simplest example Long straight wire
Right Hand Rule Trois (RHR3)
Right Hand Rule 31 Thumb in direction of
current2 Curl fingers in direction
of B field
Current Carrying Wire amp Compass
Force bw Parallel WiresHow do current carrying wires affect one another
SolenoidsAlmost like the magneto static equivalent of electrostaticsrsquo
parallel plate capacitor
Magnetic Field of Earth
Magnetic Forces IThe force acting on a moving charge in a B field is
1 proportional to the magnitude of the2 proportional to the magnitude of the3 proportional to the component of the
q
B
vθ
Right Hand Rule (RHR)DWTThe direction and the magnitude of the magnetic force is determined by a cross product computation (vector calculus ugh) Wersquoll cheat and use our hands (correction just right hand) rather than calculus
Right Hand Rule 11 Fingers in direction of B Field2 Thumb in direction of chargersquos
velocity v3a Positive Charge
Direction of Force corresponds to direction of the palm
3b Negative ChargeDirection of Force corresponds to direction of back of hand
RHR1 Examples
Notation used for Fieldsx ndash into surfacepage
(dot) ndash out of surfacepage
JJ Thomsonrsquos em RatioDWT Sir Joseph John ldquoJJrdquo Thomson (1856 ndash 1940) was a British physicist and Nobel laureate
credited for the discovery of the electron (Physics Nobel Prize in 1906) and the invention of the mass spectrometer
Thomson used a cathode ray tube to fire a stream of electrons through magnetic and electric fields (1897)
From his experiments he determined1 that there must be some small negatively charged particle (known today as
the electron JJ called them corpuscles)2 the charge to mass ratio (em ratio) of this new particle dubbed the electron
JJrsquos Cathode Ray Tube (simplified)
Actual Apparatus
Velocity Selector
Mass SpectrometerA scientific device that uses electric and
magnetic fields to determine the mass of a substance
How it Works1 Substance is ionized and vaporized2 Charged plates accelerate particles3 Particles pass through magnetic and
electric fields (velocity selector)4 Particles move in a curved path in the
presence of a magnetic field
Curved Motion Due to B FieldWhat is the radius R of the circular motion of the particle as
a result of the magnetic force
Mars RoverScientists want to include a compact mass
spectrometer on a future Mars rover Suppose the instrument is designed to have a magnetic field of 001 T and selects carbon ions that have a speed of 5 x 103 ms and are singly ionized (have a charge of +e) What are the radii R12 and R13 of the orbits of 12C and 13C ions in this spectrometer
A particle of mass m and charge ndashq is accelerated through a potential difference ε It then passes into a uniform magnetic field of magnitude B directed into the page as shown below Express your answers in terms of m q ε and B
a) Determine the speed of the electron as it enters the magnetic field
b) Sketch the path of the electron in the magnetic field on the diagram above
c) Determine the radius of the path of the electrond) An electric field E is now established in the same region
as the magnetic field so that the electron passes through the field undeflected
(i) Determine the magnitude of E(ii) Indicate the direction of E on the diagram above
Particle in Magnetic Field
Magnetic Forces IIThe force acting on a segment of conductor with length l
carrying a current I in a uniform B field is
B
θ I
l
Right Hand Rule Dos (RHR2)
Right Hand Rule 21 Fingers in direction of B Field2 Thumb in direction of
conductorrsquos current I(remember current is direction of positive charges)
3 Direction of Force corresponds to direction of the palm
B Force on Current LoopHow do the magnetic forces act on a current carrying loop
B Force on Current Loop Cont
Electric MotorsMotors operate because of the magnetic force on current carrying
conductors
Force on Conducting BarMagnetic forces are used to accelerate current carrying
conductors
B Fields From E CurrentsAn electric current creates a magnetic field
Simplest example Long straight wire
Right Hand Rule Trois (RHR3)
Right Hand Rule 31 Thumb in direction of
current2 Curl fingers in direction
of B field
Current Carrying Wire amp Compass
Force bw Parallel WiresHow do current carrying wires affect one another
SolenoidsAlmost like the magneto static equivalent of electrostaticsrsquo
parallel plate capacitor
Magnetic Forces IThe force acting on a moving charge in a B field is
1 proportional to the magnitude of the2 proportional to the magnitude of the3 proportional to the component of the
q
B
vθ
Right Hand Rule (RHR)DWTThe direction and the magnitude of the magnetic force is determined by a cross product computation (vector calculus ugh) Wersquoll cheat and use our hands (correction just right hand) rather than calculus
Right Hand Rule 11 Fingers in direction of B Field2 Thumb in direction of chargersquos
velocity v3a Positive Charge
Direction of Force corresponds to direction of the palm
3b Negative ChargeDirection of Force corresponds to direction of back of hand
RHR1 Examples
Notation used for Fieldsx ndash into surfacepage
(dot) ndash out of surfacepage
JJ Thomsonrsquos em RatioDWT Sir Joseph John ldquoJJrdquo Thomson (1856 ndash 1940) was a British physicist and Nobel laureate
credited for the discovery of the electron (Physics Nobel Prize in 1906) and the invention of the mass spectrometer
Thomson used a cathode ray tube to fire a stream of electrons through magnetic and electric fields (1897)
From his experiments he determined1 that there must be some small negatively charged particle (known today as
the electron JJ called them corpuscles)2 the charge to mass ratio (em ratio) of this new particle dubbed the electron
JJrsquos Cathode Ray Tube (simplified)
Actual Apparatus
Velocity Selector
Mass SpectrometerA scientific device that uses electric and
magnetic fields to determine the mass of a substance
How it Works1 Substance is ionized and vaporized2 Charged plates accelerate particles3 Particles pass through magnetic and
electric fields (velocity selector)4 Particles move in a curved path in the
presence of a magnetic field
Curved Motion Due to B FieldWhat is the radius R of the circular motion of the particle as
a result of the magnetic force
Mars RoverScientists want to include a compact mass
spectrometer on a future Mars rover Suppose the instrument is designed to have a magnetic field of 001 T and selects carbon ions that have a speed of 5 x 103 ms and are singly ionized (have a charge of +e) What are the radii R12 and R13 of the orbits of 12C and 13C ions in this spectrometer
A particle of mass m and charge ndashq is accelerated through a potential difference ε It then passes into a uniform magnetic field of magnitude B directed into the page as shown below Express your answers in terms of m q ε and B
a) Determine the speed of the electron as it enters the magnetic field
b) Sketch the path of the electron in the magnetic field on the diagram above
c) Determine the radius of the path of the electrond) An electric field E is now established in the same region
as the magnetic field so that the electron passes through the field undeflected
(i) Determine the magnitude of E(ii) Indicate the direction of E on the diagram above
Particle in Magnetic Field
Magnetic Forces IIThe force acting on a segment of conductor with length l
carrying a current I in a uniform B field is
B
θ I
l
Right Hand Rule Dos (RHR2)
Right Hand Rule 21 Fingers in direction of B Field2 Thumb in direction of
conductorrsquos current I(remember current is direction of positive charges)
3 Direction of Force corresponds to direction of the palm
B Force on Current LoopHow do the magnetic forces act on a current carrying loop
B Force on Current Loop Cont
Electric MotorsMotors operate because of the magnetic force on current carrying
conductors
Force on Conducting BarMagnetic forces are used to accelerate current carrying
conductors
B Fields From E CurrentsAn electric current creates a magnetic field
Simplest example Long straight wire
Right Hand Rule Trois (RHR3)
Right Hand Rule 31 Thumb in direction of
current2 Curl fingers in direction
of B field
Current Carrying Wire amp Compass
Force bw Parallel WiresHow do current carrying wires affect one another
SolenoidsAlmost like the magneto static equivalent of electrostaticsrsquo
parallel plate capacitor
Right Hand Rule (RHR)DWTThe direction and the magnitude of the magnetic force is determined by a cross product computation (vector calculus ugh) Wersquoll cheat and use our hands (correction just right hand) rather than calculus
Right Hand Rule 11 Fingers in direction of B Field2 Thumb in direction of chargersquos
velocity v3a Positive Charge
Direction of Force corresponds to direction of the palm
3b Negative ChargeDirection of Force corresponds to direction of back of hand
RHR1 Examples
Notation used for Fieldsx ndash into surfacepage
(dot) ndash out of surfacepage
JJ Thomsonrsquos em RatioDWT Sir Joseph John ldquoJJrdquo Thomson (1856 ndash 1940) was a British physicist and Nobel laureate
credited for the discovery of the electron (Physics Nobel Prize in 1906) and the invention of the mass spectrometer
Thomson used a cathode ray tube to fire a stream of electrons through magnetic and electric fields (1897)
From his experiments he determined1 that there must be some small negatively charged particle (known today as
the electron JJ called them corpuscles)2 the charge to mass ratio (em ratio) of this new particle dubbed the electron
JJrsquos Cathode Ray Tube (simplified)
Actual Apparatus
Velocity Selector
Mass SpectrometerA scientific device that uses electric and
magnetic fields to determine the mass of a substance
How it Works1 Substance is ionized and vaporized2 Charged plates accelerate particles3 Particles pass through magnetic and
electric fields (velocity selector)4 Particles move in a curved path in the
presence of a magnetic field
Curved Motion Due to B FieldWhat is the radius R of the circular motion of the particle as
a result of the magnetic force
Mars RoverScientists want to include a compact mass
spectrometer on a future Mars rover Suppose the instrument is designed to have a magnetic field of 001 T and selects carbon ions that have a speed of 5 x 103 ms and are singly ionized (have a charge of +e) What are the radii R12 and R13 of the orbits of 12C and 13C ions in this spectrometer
A particle of mass m and charge ndashq is accelerated through a potential difference ε It then passes into a uniform magnetic field of magnitude B directed into the page as shown below Express your answers in terms of m q ε and B
a) Determine the speed of the electron as it enters the magnetic field
b) Sketch the path of the electron in the magnetic field on the diagram above
c) Determine the radius of the path of the electrond) An electric field E is now established in the same region
as the magnetic field so that the electron passes through the field undeflected
(i) Determine the magnitude of E(ii) Indicate the direction of E on the diagram above
Particle in Magnetic Field
Magnetic Forces IIThe force acting on a segment of conductor with length l
carrying a current I in a uniform B field is
B
θ I
l
Right Hand Rule Dos (RHR2)
Right Hand Rule 21 Fingers in direction of B Field2 Thumb in direction of
conductorrsquos current I(remember current is direction of positive charges)
3 Direction of Force corresponds to direction of the palm
B Force on Current LoopHow do the magnetic forces act on a current carrying loop
B Force on Current Loop Cont
Electric MotorsMotors operate because of the magnetic force on current carrying
conductors
Force on Conducting BarMagnetic forces are used to accelerate current carrying
conductors
B Fields From E CurrentsAn electric current creates a magnetic field
Simplest example Long straight wire
Right Hand Rule Trois (RHR3)
Right Hand Rule 31 Thumb in direction of
current2 Curl fingers in direction
of B field
Current Carrying Wire amp Compass
Force bw Parallel WiresHow do current carrying wires affect one another
SolenoidsAlmost like the magneto static equivalent of electrostaticsrsquo
parallel plate capacitor
RHR1 Examples
Notation used for Fieldsx ndash into surfacepage
(dot) ndash out of surfacepage
JJ Thomsonrsquos em RatioDWT Sir Joseph John ldquoJJrdquo Thomson (1856 ndash 1940) was a British physicist and Nobel laureate
credited for the discovery of the electron (Physics Nobel Prize in 1906) and the invention of the mass spectrometer
Thomson used a cathode ray tube to fire a stream of electrons through magnetic and electric fields (1897)
From his experiments he determined1 that there must be some small negatively charged particle (known today as
the electron JJ called them corpuscles)2 the charge to mass ratio (em ratio) of this new particle dubbed the electron
JJrsquos Cathode Ray Tube (simplified)
Actual Apparatus
Velocity Selector
Mass SpectrometerA scientific device that uses electric and
magnetic fields to determine the mass of a substance
How it Works1 Substance is ionized and vaporized2 Charged plates accelerate particles3 Particles pass through magnetic and
electric fields (velocity selector)4 Particles move in a curved path in the
presence of a magnetic field
Curved Motion Due to B FieldWhat is the radius R of the circular motion of the particle as
a result of the magnetic force
Mars RoverScientists want to include a compact mass
spectrometer on a future Mars rover Suppose the instrument is designed to have a magnetic field of 001 T and selects carbon ions that have a speed of 5 x 103 ms and are singly ionized (have a charge of +e) What are the radii R12 and R13 of the orbits of 12C and 13C ions in this spectrometer
A particle of mass m and charge ndashq is accelerated through a potential difference ε It then passes into a uniform magnetic field of magnitude B directed into the page as shown below Express your answers in terms of m q ε and B
a) Determine the speed of the electron as it enters the magnetic field
b) Sketch the path of the electron in the magnetic field on the diagram above
c) Determine the radius of the path of the electrond) An electric field E is now established in the same region
as the magnetic field so that the electron passes through the field undeflected
(i) Determine the magnitude of E(ii) Indicate the direction of E on the diagram above
Particle in Magnetic Field
Magnetic Forces IIThe force acting on a segment of conductor with length l
carrying a current I in a uniform B field is
B
θ I
l
Right Hand Rule Dos (RHR2)
Right Hand Rule 21 Fingers in direction of B Field2 Thumb in direction of
conductorrsquos current I(remember current is direction of positive charges)
3 Direction of Force corresponds to direction of the palm
B Force on Current LoopHow do the magnetic forces act on a current carrying loop
B Force on Current Loop Cont
Electric MotorsMotors operate because of the magnetic force on current carrying
conductors
Force on Conducting BarMagnetic forces are used to accelerate current carrying
conductors
B Fields From E CurrentsAn electric current creates a magnetic field
Simplest example Long straight wire
Right Hand Rule Trois (RHR3)
Right Hand Rule 31 Thumb in direction of
current2 Curl fingers in direction
of B field
Current Carrying Wire amp Compass
Force bw Parallel WiresHow do current carrying wires affect one another
SolenoidsAlmost like the magneto static equivalent of electrostaticsrsquo
parallel plate capacitor
JJ Thomsonrsquos em RatioDWT Sir Joseph John ldquoJJrdquo Thomson (1856 ndash 1940) was a British physicist and Nobel laureate
credited for the discovery of the electron (Physics Nobel Prize in 1906) and the invention of the mass spectrometer
Thomson used a cathode ray tube to fire a stream of electrons through magnetic and electric fields (1897)
From his experiments he determined1 that there must be some small negatively charged particle (known today as
the electron JJ called them corpuscles)2 the charge to mass ratio (em ratio) of this new particle dubbed the electron
JJrsquos Cathode Ray Tube (simplified)
Actual Apparatus
Velocity Selector
Mass SpectrometerA scientific device that uses electric and
magnetic fields to determine the mass of a substance
How it Works1 Substance is ionized and vaporized2 Charged plates accelerate particles3 Particles pass through magnetic and
electric fields (velocity selector)4 Particles move in a curved path in the
presence of a magnetic field
Curved Motion Due to B FieldWhat is the radius R of the circular motion of the particle as
a result of the magnetic force
Mars RoverScientists want to include a compact mass
spectrometer on a future Mars rover Suppose the instrument is designed to have a magnetic field of 001 T and selects carbon ions that have a speed of 5 x 103 ms and are singly ionized (have a charge of +e) What are the radii R12 and R13 of the orbits of 12C and 13C ions in this spectrometer
A particle of mass m and charge ndashq is accelerated through a potential difference ε It then passes into a uniform magnetic field of magnitude B directed into the page as shown below Express your answers in terms of m q ε and B
a) Determine the speed of the electron as it enters the magnetic field
b) Sketch the path of the electron in the magnetic field on the diagram above
c) Determine the radius of the path of the electrond) An electric field E is now established in the same region
as the magnetic field so that the electron passes through the field undeflected
(i) Determine the magnitude of E(ii) Indicate the direction of E on the diagram above
Particle in Magnetic Field
Magnetic Forces IIThe force acting on a segment of conductor with length l
carrying a current I in a uniform B field is
B
θ I
l
Right Hand Rule Dos (RHR2)
Right Hand Rule 21 Fingers in direction of B Field2 Thumb in direction of
conductorrsquos current I(remember current is direction of positive charges)
3 Direction of Force corresponds to direction of the palm
B Force on Current LoopHow do the magnetic forces act on a current carrying loop
B Force on Current Loop Cont
Electric MotorsMotors operate because of the magnetic force on current carrying
conductors
Force on Conducting BarMagnetic forces are used to accelerate current carrying
conductors
B Fields From E CurrentsAn electric current creates a magnetic field
Simplest example Long straight wire
Right Hand Rule Trois (RHR3)
Right Hand Rule 31 Thumb in direction of
current2 Curl fingers in direction
of B field
Current Carrying Wire amp Compass
Force bw Parallel WiresHow do current carrying wires affect one another
SolenoidsAlmost like the magneto static equivalent of electrostaticsrsquo
parallel plate capacitor
Velocity Selector
Mass SpectrometerA scientific device that uses electric and
magnetic fields to determine the mass of a substance
How it Works1 Substance is ionized and vaporized2 Charged plates accelerate particles3 Particles pass through magnetic and
electric fields (velocity selector)4 Particles move in a curved path in the
presence of a magnetic field
Curved Motion Due to B FieldWhat is the radius R of the circular motion of the particle as
a result of the magnetic force
Mars RoverScientists want to include a compact mass
spectrometer on a future Mars rover Suppose the instrument is designed to have a magnetic field of 001 T and selects carbon ions that have a speed of 5 x 103 ms and are singly ionized (have a charge of +e) What are the radii R12 and R13 of the orbits of 12C and 13C ions in this spectrometer
A particle of mass m and charge ndashq is accelerated through a potential difference ε It then passes into a uniform magnetic field of magnitude B directed into the page as shown below Express your answers in terms of m q ε and B
a) Determine the speed of the electron as it enters the magnetic field
b) Sketch the path of the electron in the magnetic field on the diagram above
c) Determine the radius of the path of the electrond) An electric field E is now established in the same region
as the magnetic field so that the electron passes through the field undeflected
(i) Determine the magnitude of E(ii) Indicate the direction of E on the diagram above
Particle in Magnetic Field
Magnetic Forces IIThe force acting on a segment of conductor with length l
carrying a current I in a uniform B field is
B
θ I
l
Right Hand Rule Dos (RHR2)
Right Hand Rule 21 Fingers in direction of B Field2 Thumb in direction of
conductorrsquos current I(remember current is direction of positive charges)
3 Direction of Force corresponds to direction of the palm
B Force on Current LoopHow do the magnetic forces act on a current carrying loop
B Force on Current Loop Cont
Electric MotorsMotors operate because of the magnetic force on current carrying
conductors
Force on Conducting BarMagnetic forces are used to accelerate current carrying
conductors
B Fields From E CurrentsAn electric current creates a magnetic field
Simplest example Long straight wire
Right Hand Rule Trois (RHR3)
Right Hand Rule 31 Thumb in direction of
current2 Curl fingers in direction
of B field
Current Carrying Wire amp Compass
Force bw Parallel WiresHow do current carrying wires affect one another
SolenoidsAlmost like the magneto static equivalent of electrostaticsrsquo
parallel plate capacitor
Mass SpectrometerA scientific device that uses electric and
magnetic fields to determine the mass of a substance
How it Works1 Substance is ionized and vaporized2 Charged plates accelerate particles3 Particles pass through magnetic and
electric fields (velocity selector)4 Particles move in a curved path in the
presence of a magnetic field
Curved Motion Due to B FieldWhat is the radius R of the circular motion of the particle as
a result of the magnetic force
Mars RoverScientists want to include a compact mass
spectrometer on a future Mars rover Suppose the instrument is designed to have a magnetic field of 001 T and selects carbon ions that have a speed of 5 x 103 ms and are singly ionized (have a charge of +e) What are the radii R12 and R13 of the orbits of 12C and 13C ions in this spectrometer
A particle of mass m and charge ndashq is accelerated through a potential difference ε It then passes into a uniform magnetic field of magnitude B directed into the page as shown below Express your answers in terms of m q ε and B
a) Determine the speed of the electron as it enters the magnetic field
b) Sketch the path of the electron in the magnetic field on the diagram above
c) Determine the radius of the path of the electrond) An electric field E is now established in the same region
as the magnetic field so that the electron passes through the field undeflected
(i) Determine the magnitude of E(ii) Indicate the direction of E on the diagram above
Particle in Magnetic Field
Magnetic Forces IIThe force acting on a segment of conductor with length l
carrying a current I in a uniform B field is
B
θ I
l
Right Hand Rule Dos (RHR2)
Right Hand Rule 21 Fingers in direction of B Field2 Thumb in direction of
conductorrsquos current I(remember current is direction of positive charges)
3 Direction of Force corresponds to direction of the palm
B Force on Current LoopHow do the magnetic forces act on a current carrying loop
B Force on Current Loop Cont
Electric MotorsMotors operate because of the magnetic force on current carrying
conductors
Force on Conducting BarMagnetic forces are used to accelerate current carrying
conductors
B Fields From E CurrentsAn electric current creates a magnetic field
Simplest example Long straight wire
Right Hand Rule Trois (RHR3)
Right Hand Rule 31 Thumb in direction of
current2 Curl fingers in direction
of B field
Current Carrying Wire amp Compass
Force bw Parallel WiresHow do current carrying wires affect one another
SolenoidsAlmost like the magneto static equivalent of electrostaticsrsquo
parallel plate capacitor
Curved Motion Due to B FieldWhat is the radius R of the circular motion of the particle as
a result of the magnetic force
Mars RoverScientists want to include a compact mass
spectrometer on a future Mars rover Suppose the instrument is designed to have a magnetic field of 001 T and selects carbon ions that have a speed of 5 x 103 ms and are singly ionized (have a charge of +e) What are the radii R12 and R13 of the orbits of 12C and 13C ions in this spectrometer
A particle of mass m and charge ndashq is accelerated through a potential difference ε It then passes into a uniform magnetic field of magnitude B directed into the page as shown below Express your answers in terms of m q ε and B
a) Determine the speed of the electron as it enters the magnetic field
b) Sketch the path of the electron in the magnetic field on the diagram above
c) Determine the radius of the path of the electrond) An electric field E is now established in the same region
as the magnetic field so that the electron passes through the field undeflected
(i) Determine the magnitude of E(ii) Indicate the direction of E on the diagram above
Particle in Magnetic Field
Magnetic Forces IIThe force acting on a segment of conductor with length l
carrying a current I in a uniform B field is
B
θ I
l
Right Hand Rule Dos (RHR2)
Right Hand Rule 21 Fingers in direction of B Field2 Thumb in direction of
conductorrsquos current I(remember current is direction of positive charges)
3 Direction of Force corresponds to direction of the palm
B Force on Current LoopHow do the magnetic forces act on a current carrying loop
B Force on Current Loop Cont
Electric MotorsMotors operate because of the magnetic force on current carrying
conductors
Force on Conducting BarMagnetic forces are used to accelerate current carrying
conductors
B Fields From E CurrentsAn electric current creates a magnetic field
Simplest example Long straight wire
Right Hand Rule Trois (RHR3)
Right Hand Rule 31 Thumb in direction of
current2 Curl fingers in direction
of B field
Current Carrying Wire amp Compass
Force bw Parallel WiresHow do current carrying wires affect one another
SolenoidsAlmost like the magneto static equivalent of electrostaticsrsquo
parallel plate capacitor
Mars RoverScientists want to include a compact mass
spectrometer on a future Mars rover Suppose the instrument is designed to have a magnetic field of 001 T and selects carbon ions that have a speed of 5 x 103 ms and are singly ionized (have a charge of +e) What are the radii R12 and R13 of the orbits of 12C and 13C ions in this spectrometer
A particle of mass m and charge ndashq is accelerated through a potential difference ε It then passes into a uniform magnetic field of magnitude B directed into the page as shown below Express your answers in terms of m q ε and B
a) Determine the speed of the electron as it enters the magnetic field
b) Sketch the path of the electron in the magnetic field on the diagram above
c) Determine the radius of the path of the electrond) An electric field E is now established in the same region
as the magnetic field so that the electron passes through the field undeflected
(i) Determine the magnitude of E(ii) Indicate the direction of E on the diagram above
Particle in Magnetic Field
Magnetic Forces IIThe force acting on a segment of conductor with length l
carrying a current I in a uniform B field is
B
θ I
l
Right Hand Rule Dos (RHR2)
Right Hand Rule 21 Fingers in direction of B Field2 Thumb in direction of
conductorrsquos current I(remember current is direction of positive charges)
3 Direction of Force corresponds to direction of the palm
B Force on Current LoopHow do the magnetic forces act on a current carrying loop
B Force on Current Loop Cont
Electric MotorsMotors operate because of the magnetic force on current carrying
conductors
Force on Conducting BarMagnetic forces are used to accelerate current carrying
conductors
B Fields From E CurrentsAn electric current creates a magnetic field
Simplest example Long straight wire
Right Hand Rule Trois (RHR3)
Right Hand Rule 31 Thumb in direction of
current2 Curl fingers in direction
of B field
Current Carrying Wire amp Compass
Force bw Parallel WiresHow do current carrying wires affect one another
SolenoidsAlmost like the magneto static equivalent of electrostaticsrsquo
parallel plate capacitor
A particle of mass m and charge ndashq is accelerated through a potential difference ε It then passes into a uniform magnetic field of magnitude B directed into the page as shown below Express your answers in terms of m q ε and B
a) Determine the speed of the electron as it enters the magnetic field
b) Sketch the path of the electron in the magnetic field on the diagram above
c) Determine the radius of the path of the electrond) An electric field E is now established in the same region
as the magnetic field so that the electron passes through the field undeflected
(i) Determine the magnitude of E(ii) Indicate the direction of E on the diagram above
Particle in Magnetic Field
Magnetic Forces IIThe force acting on a segment of conductor with length l
carrying a current I in a uniform B field is
B
θ I
l
Right Hand Rule Dos (RHR2)
Right Hand Rule 21 Fingers in direction of B Field2 Thumb in direction of
conductorrsquos current I(remember current is direction of positive charges)
3 Direction of Force corresponds to direction of the palm
B Force on Current LoopHow do the magnetic forces act on a current carrying loop
B Force on Current Loop Cont
Electric MotorsMotors operate because of the magnetic force on current carrying
conductors
Force on Conducting BarMagnetic forces are used to accelerate current carrying
conductors
B Fields From E CurrentsAn electric current creates a magnetic field
Simplest example Long straight wire
Right Hand Rule Trois (RHR3)
Right Hand Rule 31 Thumb in direction of
current2 Curl fingers in direction
of B field
Current Carrying Wire amp Compass
Force bw Parallel WiresHow do current carrying wires affect one another
SolenoidsAlmost like the magneto static equivalent of electrostaticsrsquo
parallel plate capacitor
Magnetic Forces IIThe force acting on a segment of conductor with length l
carrying a current I in a uniform B field is
B
θ I
l
Right Hand Rule Dos (RHR2)
Right Hand Rule 21 Fingers in direction of B Field2 Thumb in direction of
conductorrsquos current I(remember current is direction of positive charges)
3 Direction of Force corresponds to direction of the palm
B Force on Current LoopHow do the magnetic forces act on a current carrying loop
B Force on Current Loop Cont
Electric MotorsMotors operate because of the magnetic force on current carrying
conductors
Force on Conducting BarMagnetic forces are used to accelerate current carrying
conductors
B Fields From E CurrentsAn electric current creates a magnetic field
Simplest example Long straight wire
Right Hand Rule Trois (RHR3)
Right Hand Rule 31 Thumb in direction of
current2 Curl fingers in direction
of B field
Current Carrying Wire amp Compass
Force bw Parallel WiresHow do current carrying wires affect one another
SolenoidsAlmost like the magneto static equivalent of electrostaticsrsquo
parallel plate capacitor
Right Hand Rule Dos (RHR2)
Right Hand Rule 21 Fingers in direction of B Field2 Thumb in direction of
conductorrsquos current I(remember current is direction of positive charges)
3 Direction of Force corresponds to direction of the palm
B Force on Current LoopHow do the magnetic forces act on a current carrying loop
B Force on Current Loop Cont
Electric MotorsMotors operate because of the magnetic force on current carrying
conductors
Force on Conducting BarMagnetic forces are used to accelerate current carrying
conductors
B Fields From E CurrentsAn electric current creates a magnetic field
Simplest example Long straight wire
Right Hand Rule Trois (RHR3)
Right Hand Rule 31 Thumb in direction of
current2 Curl fingers in direction
of B field
Current Carrying Wire amp Compass
Force bw Parallel WiresHow do current carrying wires affect one another
SolenoidsAlmost like the magneto static equivalent of electrostaticsrsquo
parallel plate capacitor
B Force on Current LoopHow do the magnetic forces act on a current carrying loop
B Force on Current Loop Cont
Electric MotorsMotors operate because of the magnetic force on current carrying
conductors
Force on Conducting BarMagnetic forces are used to accelerate current carrying
conductors
B Fields From E CurrentsAn electric current creates a magnetic field
Simplest example Long straight wire
Right Hand Rule Trois (RHR3)
Right Hand Rule 31 Thumb in direction of
current2 Curl fingers in direction
of B field
Current Carrying Wire amp Compass
Force bw Parallel WiresHow do current carrying wires affect one another
SolenoidsAlmost like the magneto static equivalent of electrostaticsrsquo
parallel plate capacitor
B Force on Current Loop Cont
Electric MotorsMotors operate because of the magnetic force on current carrying
conductors
Force on Conducting BarMagnetic forces are used to accelerate current carrying
conductors
B Fields From E CurrentsAn electric current creates a magnetic field
Simplest example Long straight wire
Right Hand Rule Trois (RHR3)
Right Hand Rule 31 Thumb in direction of
current2 Curl fingers in direction
of B field
Current Carrying Wire amp Compass
Force bw Parallel WiresHow do current carrying wires affect one another
SolenoidsAlmost like the magneto static equivalent of electrostaticsrsquo
parallel plate capacitor
Electric MotorsMotors operate because of the magnetic force on current carrying
conductors
Force on Conducting BarMagnetic forces are used to accelerate current carrying
conductors
B Fields From E CurrentsAn electric current creates a magnetic field
Simplest example Long straight wire
Right Hand Rule Trois (RHR3)
Right Hand Rule 31 Thumb in direction of
current2 Curl fingers in direction
of B field
Current Carrying Wire amp Compass
Force bw Parallel WiresHow do current carrying wires affect one another
SolenoidsAlmost like the magneto static equivalent of electrostaticsrsquo
parallel plate capacitor
Force on Conducting BarMagnetic forces are used to accelerate current carrying
conductors
B Fields From E CurrentsAn electric current creates a magnetic field
Simplest example Long straight wire
Right Hand Rule Trois (RHR3)
Right Hand Rule 31 Thumb in direction of
current2 Curl fingers in direction
of B field
Current Carrying Wire amp Compass
Force bw Parallel WiresHow do current carrying wires affect one another
SolenoidsAlmost like the magneto static equivalent of electrostaticsrsquo
parallel plate capacitor
B Fields From E CurrentsAn electric current creates a magnetic field
Simplest example Long straight wire
Right Hand Rule Trois (RHR3)
Right Hand Rule 31 Thumb in direction of
current2 Curl fingers in direction
of B field
Current Carrying Wire amp Compass
Force bw Parallel WiresHow do current carrying wires affect one another
SolenoidsAlmost like the magneto static equivalent of electrostaticsrsquo
parallel plate capacitor
Right Hand Rule Trois (RHR3)
Right Hand Rule 31 Thumb in direction of
current2 Curl fingers in direction
of B field
Current Carrying Wire amp Compass
Force bw Parallel WiresHow do current carrying wires affect one another
SolenoidsAlmost like the magneto static equivalent of electrostaticsrsquo
parallel plate capacitor
Current Carrying Wire amp Compass
Force bw Parallel WiresHow do current carrying wires affect one another
SolenoidsAlmost like the magneto static equivalent of electrostaticsrsquo
parallel plate capacitor
Force bw Parallel WiresHow do current carrying wires affect one another
SolenoidsAlmost like the magneto static equivalent of electrostaticsrsquo
parallel plate capacitor
SolenoidsAlmost like the magneto static equivalent of electrostaticsrsquo
parallel plate capacitor
