Ch29 Magnetic Fields

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Magnetic Field and Magnetic Force v F , q B B v F F , B B 0 // B F B v v B F , 0 B v F , 0 q B v F , 0 q B sin B F B v +q F B opposite direction

Transcript of Ch29 Magnetic Fields

Magnetic Field and Magnetic Force

vF ,qB

BvFF ,BB

0// BFBv

vBF ,0 B

vF ,0qB vF ,0qB

sinBF

B

v+q

FB

oppositedirection

Magnetic Force

BvF qB

sinvBqFB

Tesla (T)=N/(C.m/s)=N/(A.m)

Electric and Magnetic Forces

Electric forces act in the direction of the electric field, magnetic forces are perpendicular to the magnetic field.

A magnetic force exists only for charges in motion. The magnetic force of a steady magnetic field

does no work when displacing a charged particle. The magnetic field can alter the direction of a

moving charged particle but not it speed or its kinetic energy.

BvF qB EF qE

Magnetic Force on a Current Carrying Conductor Magnetic force acts upon charges moving

in a conductor. The total force on the current is the integral

sum of the force on each charge in the current.

In turn, the charges transfer the force on to the wire when they collide with the atoms of the wire.

Drawing the Magnetic Field

Perspective View Flat (plane) View

Magnetic Force on a Current Carrying Conductor

Magnetic Force on a Current Carrying Conductor

BvF dqB q,

nALq dB BvF

qnAvI d

BLF IBFor a straight wire in a uniform field

BsF Idd B

b

aB dI BsF

For an arbitrary wire in an arbitrary field

A Special Case – arbitrary wire in a uniform field

b

aB dI BsF

BsF

b

aB dI

BLF IB

Closed Loop in a Magnetic Field

BsF dIB

0 sd0BF

Net magnetic force acting on any closed current loop in a uniform magnetic field is zero.

Forces on a Semicircular Conductor

IRBILBF 21

On the straight wire

dsIBdIdF sin2 Bs

On the curved wire

RddsRs

dIRBdF sin2

00

2 sinsin dIRBdIRBF

IRBF 22

Directed out of the board

Directed in to the board

021 FFF

Torque on a Current Loop in a Uniform Magnetic Field

00

BFBL

For 1 and 3,

IaBFF 42

bIaB

bIaBbIaBbFbF

max

42max 2222

If the field is parallel to the plane of the loop

IABmax

For 2 and 4,

Torque on a Current Loop in a Uniform Magnetic Field

If the field makes an angle with a line perpendicular to the plane of the loop:

042 FF

sin

sinsin2

sin2

sin2

sin2 31

IAB

IabBaIbBaIbB

aFaF

BAI

Concept QuestionA rectangular loop is placed in a uniform magnetic field with the plane of the loop perpendicular to the direction of the field.If a current is made to flow through the loop in the sense shown by the arrows, the field exerts on the loop:

1. a net force.2. a net torque.3. a net force and a net torque.4. neither a net force nor a net torque.

Magnetic Dipole MomentAμ I

(Amperes.m2)

If the wire makes N loops around A,

BμBμ coilloopN

Bμ U

The potential energy of the loop is:

Motion of Charged Particles in a Uniform Magnetic Field

Consider a positive charge moving perpendicular to a magnetic field with an initial velocity, v.The force FB is always at right angles to v and its magnitude is,

qvBFB

So, as q moves, it will rotate about a circle and FB and v will always be perpendicular. The magnitude of v will always be the same, only its direction will change.

Cyclotron FrequencyTo find the radius and frequency of the rotation:

rmaF

rvmqvBFB2

qBmvr

mqB

rv

qBm

vrT

222

The radial force

The angular speed

The period

Cyclotron frequency

Helical MotionIf the initial velocity makes an arbitrary angle with B,

vx = constantvy and vz change in timeThe resulting motion is a helix

The equations for the cyclotron frequency and rotation period still apply provided, 22

zy vvv

Concept QuestionCosmic rays (atomic nuclei stripped bare of their electrons) would continuously bombard Earth’s surface if most of them were not deflected by Earth’s magnetic field. Given that Earth is, to an excellent approximation, a magnetic dipole, the intensity of cosmic rays bombarding its surface is greatest at the

1. poles.2. mid-latitudes.3. equator.

Hall EffectBvEqEBqv

dH

Hd

BdvV dH

nqAIvd

tIBR

nqtIBV H

H

Summary The right hand rule Magnetic forces on charged particles and

current carrying wires Torque on loops and magnetic dipole

moments Charged particle motion

For Next Class Reading Assignment

Chapter 30 – Sources of the Magnetic Field WebAssign: Assignment 7