Lecture4 (Chap 4)

7/28/2019 Lecture4 (Chap 4)

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Topic 4 : MAGNETIC FORCES AND MAGNETIC FIELDS

• Magnetic Fields

• The Force that a Magnetic Field Exerts on a Moving

Charge

• The Motion of a Charged Particle in a Magnetic Field

• The Force on a Current in a Magnetic Field

• The Torque on a Current-Carrying Coil

• Magnetic Field Produced by Currents

• Ampere’s Law

• Electromagnetic Induction

• Mutual-Inductance and Self-Inductance

• Transformer



21.1 Magnetic Fields

The needle of a compass is permanent magnet that has a northmagnetic pole (N) at one end and a south magnetic pole (S) at

the other.




The behavior of magnetic

poles is similar to that of

like and unlike electric charges.




Surrounding a magnet there is a magnetic f ie ld . The direction

of the magnetic field at any point in space is the direction indicated

by the north pole of a small compass needle placed at that point.




The magnetic field lines and pattern of iron filings in the vicinity of a

bar magnet and the magnetic field lines in the gap of a horseshoe

magnet.



21.2 The Force That a Magnetic Field Exerts o n a Charge

The following conditions must be met for a charge to experience

a magnetic force when placed in a magnetic field:

1. The charge must be moving.

2. The velocity of the charge must have a component that is

perpendicular to the direction of the magnetic field.




Righ t Hand Ru le No. 1. Extend the right hand so the fingers point

along the direction of the magnetic field and the thumb points along

the velocity of the charge. The palm of the hand then faces in the

direction of the magnetic force that acts on a positive charge.

If the moving charge is negative,

the direction of the force is opposite

to that predicted by RHR-1.




DEFINITION OF THE MAGNETIC FIELD

The magnitude of the magnetic field at any point in space is definedas

sinvq

F B

o

where the angle (0<θ<180o) is the angle between the velocity of

the charge and the direction of the magnetic field.

SI Unit o f Magnetic Field: Ttesla1

meter coulomb

secondnewton

tesla10gauss1 4




Example 1 Magnetic Forces on Charged Particles

A proton in a particle accelerator has a speed of 5.0x106 m/s. The proton

encounters a magnetic field whose magnitude is 0.40 T and whose directionmakes and angle of 30.0 degrees with respect to the proton’s velocity

(see part (c) of the figure). Find (a) the magnitude and direction of the

force on the proton and (b) the acceleration of the proton. (c) What would

be the force and acceleration of the particle were an electron?




N106.1

0.30sinT40.0sm100.5C1060.1sin

13

619

vBq F o(a)

(b)

(c)

213

27

13

p

sm106.9kg1067.1

N106.1

m

F a

Magnitude is the same, but direction is opposite.

217

31

13

e

sm108.1kg1011.9

N106.1

m

F a



21.3 The Motion of a Charged Part icle in a Magnetic Field

Conceptual Examp le 2 A Velocity Selector

A velocity selector is a device for measuring

the velocity of a charged particle. The device

operates by applying electric and magnetic

forces to the particle in such a way that these

forces balance.

How should an electric field be applied so that

the force it applies to the particle can balance

the magnetic force?



Exercise 1

Find the direction of the magnetic field acting on the

positively charged particle moving in the various

situations shown in figure below, if the direction of the

magnetic force acting on it is as indicated.

Into the page Towards bottom of the pageTowards the right



21.3 The Motion of a Charged Part icle in a Magnetic Field

The electrical force can do work on a

charged particle.

The magnetic force cannot do work on a

charged particle.

C



21.5 The Force on a Curren t in a Magnetic Field

The magnetic force on the

moving charges pushes the

wire to the right.

21 5 Th F C t i M ti Fi ld




sinqvB F

sin Bt vt

q

F L

I

sin ILB F





Example 5 The Force and Acceleration in a Loudspeaker

The voice coil of a speaker has a diameter of 0.0025 m, contains 55 turns of

wire, and is placed in a 0.10-T magnetic field. The current in the voice coil is2.0 A. (a) Determine the magnetic force that acts on the coil and the

cone. (b) The voice coil and cone have a combined mass of 0.0200 kg. Find

their acceleration.





(a)

N86.0

90sinT10.0m0025.055A0.2

sin

ILB F

(b)2sm43

kg020.0

N86.0

m

F a



Exercise 2

A current I = 15 A is directed along the positive x axis

and perpendicularly to a magnetic field. The conductor

experiences a magnetic force per unit length of 0.12 N/m

in the negative y direction. Calculate the magnitude and

direction of the magnetic field in the region throughwhich the current passes.

The direction of B:

0.12 N m

sin 15 A sin90

F LB

I

38.0 10 T

the directionz

21 6 The Torq ue on a Current Carrying Co il



21.6 The Torq ue on a Current-Carrying Co il

The two forces on the loop have equal magnitude but an application

of RHR-1 shows that they are opposite in direction.





The loop tends to rotate such that its

normal becomes aligned with the magneticfield.





sinsinsin Net torque21

21 IABw ILBw ILB

sin

momentmagnetic

B NIA

number of turns of wire





Examp le 6 The Torque Exerted on a Current-Carrying Coil

A coil of wire has an area of 2.0x10-4m2, consists of 100 loops or turns,

and contains a current of 0.045 A. The coil is placed in a uniform magnetic

field of magnitude 0.15 T. (a) Determine the magnetic moment of the coil.

(b)Find the maximum torque that the magnetic field can exert on the

coil.

(a)

2424

momentmagnetic

mA100.9m100.2A045.0100 NIA

m N104.190sinT15.0mA100.9sin 424

momentmagnetic

B NIA(b)

21 7 Magnet ic Fie lds Produc ed by Currents



21.7 Magnet ic Fie lds Produc ed by Currents

Righ t-Hand Ru le No. 2. Curl the fingers of the

right hand into the shape of a half-circle. Point

the thumb in the direction of the conventional

current, and the tips of the fingers will point

in the direction of the magnetic field.





A LONG, STRAIGHT WIRE

r

I B

o

2

AmT104 7 o

permeability of

free space





Example 7 A Current Exerts a Magnetic Force on a Moving Charge

The long straight wire carries a current

of 3.0 A. A particle has a charge of

+6.5x10-6 C and is moving parallel to

the wire at a distance of 0.050 m. The

speed of the particle is 280 m/s.

Determine the magnitude and direction

of the magnetic force on the particle.





sin2

sin

r

I qvqvB F o

r

I B

o

2





Current carrying wires can exert forces on each other.





Conceptual Examp le 9 The Net Force That a Current-Carrying Wire

Exerts on a Current Carrying Coil

Is the coil attracted to, or repelled by the wire?





A LOOP OF WIRE

center of circular loop

R

I B

o

2




g y

The field lines around the bar magnet resemble those around the loop.




g y




g y

A SOLENOID

Inter ior of a soleno id nI B o

number of turns per

unit length

21.8 Ampere’s Law



p

AMPERE’S LAW FOR STATIC MAGNETIC FIELDS

For any current geometry that produces a

magnetic field that does not change in time,

I B o ||

net current

passing through

surface bounded

by path

21.8 Ampere’s Law



p

Examp le 11 An Infinitely Long, Straight, Current-Carrying Wire

Use Ampere’s law to obtain the magnetic field.

I B o ||

I B o

I r B o 2

r

I B

o

2

22.1 Induc ed Emf and Induced Current



There are a number of ways a magnetic field can be used to

generate an electric current.

It is the changing field that produces the current.

22.1 Induc ed Emf and Induced Current



The current in the coil is called the induced cu rrent because it is brought

about by a changing magnetic field.

Since a source emf is always needed to produce a current, the coil behavesas if it were a source of emf. This emf is known as the induced emf.

The phenomena of producing an induced emf with the aid of a magnetic

field is called electromagnet ic induct ion.

22.8 Mutual Inductance and Sel f Indu ctance



MUTUAL INDUCTANCE

The changing current in the primary coil creates a changing

magnetic flux through the secondary coil, which leads to an

induced emf in the secondary coil.

The effect in called

mu tual induct ion.




Emf due to mutual induct ion

t

I M S

p

mutual inductance

SI Unit of mutual inductanc e: (Henry) H1As1V

t

N s

sS




SELF INDUCTANCE

The effect in which a changing current in a circuit induces and emf

in the same circuit is referred to as sel f induct ion .




SI Unit of self ind uctanc e: (Henry) H1As1V

t

I L

self inductance




THE ENERGY STORED IN AN INDUCTOR

Energy stored in

an induc tor

Energy density

2

21Energy LI

2

2

1densityEnergy B

o



Exercise 3

A coil of wire with a resistance of 0.45 has a

self-inductance of 0.083 H. If a 6.0-V battery is

connected across the ends of the coil and the

current in the circuit reaches an equilibriumvalue, what is the stored energy in the inductor?

Answer: 7.38 J

22.9 Transformers



A t ransformer is a device for increasing or decreasing an ac

voltage.

t N

ss

t N

p p

p

s

p

s

N

N

p

s

N

N turns ratio

22.9 Transformers



p

s

p

s

N

N

V

V

Transformer

equat ion

22.9 Transformers



s

p

s

p

p

s

N

N

V

V

I

I

A transformer that steps up the voltage simultaneously steps

down the current, and a transformer that steps down the voltage

steps up the current.



Exercise 4

A transformer changes 120 V across the

primary to 1200 V across the secondary.

If the secondary coil has 800 turns, how

many turns does the primary coil have?

Answer: 80

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Lecture4 (Chap 4)