20 Magnetic Field & Forces

Magnetism

S

N

S

N

Extended…

Magnetic Field & ForceAnalogous to Electric Field– Moving charge or current creates magnetic fieldMagnetic field exerts a force on any other moving charge or currentNo magnetic monopole !

Static Charge ~ E-field Moving Charge ~ B-field(any E-field here?)

More Magnetic Fields

Magnetic Field Lines

Closed loopsOutside NSInside SN

Direction &Magnitude(similar to E filed)

Magnetic Field Lines

Micro Picture of Magnet

Magnetic Forces & Right-hand Rule

A charged particle with velocity v in magnetic field B, then we have the force on the particle, F:

Magnitude

Direction Right-hand Rule

For current with length l

[B] in Tesla: 1 T = 1N/(A.m)

BvqF

sinvBqF

B

F

v

+q

IlBF

Right-hand Rule: + & -charges

Right-hand Rule: Current & Centripetal Force

FieldDirection (B)

CurrentDirection (v)

Motion of Charged Particle in B-field  

qB

m

v

RT

qB

mvR

R

vmmaqvBF

22

2

Helical Motion and Auroras

No magnetic force on the direction parallel to the B-field.

Magnetic Force on Current

IlBBt

ltIQvBF

)(

More general

sinIlBF

Application: Magnetic Rail Gun

Force & Torque on Current Loop

Application: DC Motor

Permeability of vacuum

B-field: Long Straight Current

T.m/A70

0

104

2

r

IB

B-field: Current Loops & Solenoids

nIB

R

NIB

R

IB

0

0

0

2

2

B-field at the center of loop

(1 turn)

(N turns)

(n: turns per unitlength)

Force between Parallel Conductor

I I’

r

II

l

F

lBIFr

IB

2

'

'2

0

0

*Introduction: Biot-Savart Law & Ampere’s Law

IsB

r

lIB

0

20 sin

4

l

B

r

I

B

s

Summary: B-field & Force

Summary: Charged Particle in B-field

Summary: Force on Current-Carrying Conductor

Summary: Force, Torque, & Motor

Summary: B-field Generation

Summary: Current Loop & Solenoids

Summary: B-field Calculation

IsB

r

lIB

0

20 sin

4

l

B

r

I

B

s

Biot-Savart Law

Ampere’s law

HomeworkCh20: 1, 4, 13, 17, 26, 31, 34, 40, 54, 58.

Galvanometer

Right-hand Rule

Charged particle/current in B-filed: determine forceForce q(sign) . Velocity x B-field

Determine B-filed from the currentB-field Current(l) x Position (r)

Q2 & Q3

Q7

P31

P34