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7/22/2019 AP Physics B - Magnetic Fields and Forces
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Magnetic Fields and Forces
AP Physics B
7/22/2019 AP Physics B - Magnetic Fields and Forces
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Facts about Magnetism Magnets have 2 poles
(north and south)
Like poles repel
Unlike poles attract
Magnets create aMAGNETIC FIELDaround them
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Magnetic FieldA bar magnet has a magnetic field
around it. This field is 3D in natureand often represented by lines
LEAVING north and ENTERINGsouth
To define a magnetic field you need
to understand the MAGNITUDEand DIRECTION
We sometimes call the magnetic fielda B-Field as the letter B is theSYMBOL for a magnetic field withthe TESLA (T) as the unit.
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Magnetic Force on a moving chargeIf a MOVING CHARGEmoves into a magneticfield it will experience aMAGNETIC FORCE.This deflection is 3D innature.
N
N
S
S
-
vo
B
sinqvBF
BvqF
B
B
=
=r
r
r The conditions for the force are:
Must have a magnetic field presentCharge must be movingCharge must be positive or negative
Charge must be movingPERPENDICULAR to the field.
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ExampleA proton moves with a speed of 1.0x105 m/s through the Earths magnetic field,which has a value of 55T at a particular location. When the proton moveseastward, the magnetic force is a maximum, and when it moves northward, nomagnetic force acts upon it. What is the magnitude and direction of the magnetic
force acting on the proton?
==
===
B
B
B
F
xxxF
qvBF
)1055)(100.1)(106.1(
190sin,90,
6519
8.8x10-19 N
The direction cannot be determined precisely by the given information. Since
no force acts on the proton when it moves northward (meaning the angle isequal to ZERO), we can infer that the magnetic field must either go northwardor southward.
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Direction of the magnetic force?
Right Hand Rule To determine the DIRECTION of theforce on a POSITIVE charge weuse a special technique that
helps us understand the3D/perpendicular nature ofmagnetic fields.
Basically you hold your right
hand flat with your thumbperpendicular to the rest of your
fingers
The Fingers = Direction B-Field
The Thumb = Direction of velocityThe Palm = Direction of the Force
For NEGATIVE charges use left hand!
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ExampleDetermine the direction of the unknown variable for a protonmoving in the field using the coordinate axis given
+y
+x+z
B = -xv = +yF =+z
B =+Z
v = +xF =-y
B = -zv = +yF =-x
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ExampleDetermine the direction of the unknown variablefor an electron using the coordinate axis given.
+y
+x+z
B = +xv = +yF =+z
B =v = - xF = +y
-z
F
B
B = +z
v =F = +y+x
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Magnetic Force and Circular MotionX X X X X X X X X
X X X X X X X X X
X X X X X X X X X
X X X X X X X X X
vB
- -
FB
FB
FB
FB -
-
-
Suppose we have an electron
traveling at a velocity , v, entering
a magnetic field, B, directed into
the page. What happens after theinitial force acts on the charge?
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Magnetic Force and Circular MotionThe magnetic force is equal to the
centripetal force and thus can be usedto solve for the circular path. Or, if the
radius is known, could be used tosolve for the MASS of the ion. This
could be used to determine the
material of the object.
There are many other types of
forces that can be set equal to themagnetic force.
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Example
?
5.0
250
105.2
106.1
26
19
=
=
=
=
=
r
TB
VV
kgxm
Cxq
qB
mvr
r
mvqvBFF cB ===
2
==
=
=
==
26
19
2
105.2
)106.1)(250(22
21
x
x
m
Vqv
q
mv
q
K
q
WV
A singly charged positive ion has a mass of 2.5 x 10-26kg. After being
accelerated through a potential difference of 250 V, the ion enters amagnetic field of 0.5 T, in a direction perpendicular to the field.
Calculate the radius of the path of the ion in the field.
We need to
solve for thevelocity!
56,568 m/s
==
)5.0)(106.1(
)568,56)(105.2(19
26
x
xr 0.0177 m
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Mass SpectrometersMass spectrometry is an analytical technique that identifies thechemical composition of a compound or sample based on themass-to-charge ratio of charged particles. A sample undergoeschemical fragmentation, thereby forming charged particles (ions).The ratio of charge to mass of the particles is calculated bypassing them through ELECTRIC and MAGNETIC fields in amass spectrometer.
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M.S. Area 1 The Velocity Selector
BEvvBE
qEqvBFF EB
==
==When you inject the sample you want it
to go STRAIGHT through the plates.Since you have an electric field youalso need a magnetic field to apply a
force in such a way as to CANCEL outthe electric force caused by the electric
field.
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M.S. Area 2 Detector RegionAfter leaving region 1 in a straight line, it
enters region 2, which ONLY has a magneticfield. This field causes the ion to move in a
circle separating the ions separate by mass.This is also where the charge to mass ratiocan then by calculated. From that point,
analyzing the data can lead to identifyingunknown samples.
r
Bv
m
q
r
mvqvBFF cB
=
==2
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Charges moving in a wire
Up to this point we have focused our attention onPARTICLES or CHARGES only. The charges couldbe moving together in a wire. Thus, if the wire had aCURRENT (moving charges), it too will experience aforce when placed in a magnetic field.
You simply used the RIGHT
HAND ONLY and the thumb
will represent the direction ofthe CURRENT instead of thevelocity.
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Charges moving in a wire
sin
sin))((
sin
ILBF
Bvtt
qF
t
tqvBF
B
B
B
=
=
=
At this point it is VERY important that
you understand that the MAGNETICFIELD is being produced by someEXTERNAL AGENT
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ExampleA 36-m length wire carries a current
of 22A running from right to left.Calculate the magnitude anddirection of the magnetic force
acting on the wire if it is placed in amagnetic field with a magnitude of
0.50 x10-4 T and directed up thepage.
=
=
=
B
B
B
F
xF
ILBF
90sin)1050.0)(36)(22(
sin4
0.0396 N
B = +yI = -xF =
+y
+x+z
-z, into the page
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WHY does the wire move?The real question is WHY does the wire move? It is easy to
say the EXTERNAL field moved it. But how can an externalmagnetic field FORCE the wire to move in a certaindirection?
THE WIRE ITSELF MUST BE MAGNETIC!!! In other words the wire has its
own INTERNAL MAGNETIC FIELD that is attracted or repulsed by theEXTERNAL FIELD.
As it turns out, the wires OWN internal magnetic
field makes concentric circles round the wire.
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A current carrying wires INTERNAL
magnetic fieldTo figure out the DIRECTION of this
INTERNAL field you use the right
hand rule. You point your thumb inthe direction of the current thenCURL your fingers. Your fingers willpoint in the direction of the magneticfield
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The MAGNITUDE of the internal field
The magnetic field, B, is directly proportional
to the current, I, and inversely proportional
to the circumference.
r
IB
A
Tmxx
r
IB
rBIB
o
o
2
)1026.1(104
constanttypermeabilivacuum
alityproportionofconstant
2
2
1
internal
67
o
o
=
=
=
=
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ExampleA long, straight wires carries a current of 5.00 A. At one instant, a
proton, 4 mm from the wire travels at 1500 m/s parallel to thewire and in the same direction as the current. Find themagnitude and direction of the magnetic force acting on the
proton due to the field caused by the current carrying wire.
==
==
==
))(1500)(106.1(
)004.0)(14.3(2)5)(1026.1(
2
19
6
wireB
IN
oINEXB
BxF
xB
r
IBqvBF
5A
4mm+
v
2.51 x 10- 4 T
6.02 x 10- 20 N
X X X
X X X
X X X
X X XX X X
X X X
B = +zv = +yF = -x