Magnetic field II

Plan• Motion of charge particle in

electric and magnetic fields

• Some applications of magnetic fields

Force due to magnetic field

BvqFB

BlIdFB

Recap………

Work done by FB

Magnetic forces can only alter the direction

0W

Recap………

Lorentz force

)( BvqEqF

Recap………

Combined E and B fields

Acts on any particle, whether moving or in rest

Acts on moving particle only

)( BvqEqF

Motion of charge particle in the

crossed B and E fields

B

Ev

Particle for which v = E/B, passes un deflected. Particles with other fields are deflected.

vBE

If

Calculation of e/m for electron

Motion of charged particle in constant uniform

Electric field

Neglecting gravity 2

2

2

1

xy

v

x

m

eEY

A Parabolic

path

tvx 2

2

1aty

mgeEma

• Substituting Lxand

B

Ev

22

2

LB

yE

m

e

kgCm

e/107.1 11

2

2

2

1

xy

v

x

m

eEY

Constant uniform Magnetic field

• B does not change the speed

• It changes direction of motion

• Thus particle should move in a circle, if moves in a plane perpendicular to B.

r

vmBvq

2

|| Bq

mvr

||

x x

x x

x

x

x

x

x x x x

x x x xx

x

x

x

x x x x x

x x x x x

x

x

x

x

x

x

FB

Bq

mvr

||

Angular frequency

m

qBf

m

Bq

r

v

22

x x

x x

x

x

x

x

x x x x

x x x xx

x

x

x

x x x x x

x x x x x

x

x

x

x

x

x

FB

x x

x x

x

x

x

x

x x x x

x x x xx

x

x

x

x x x x x

x x x x x

x

x

x

x

x

x

FB

Applications of magnetic fields

Application I- Mass spectrometer

R mTo separate the ionized atoms

Application II - Cyclotron

m

RBqmvK

22

1 2222

E. O. Lawerence

(1930)

World’s largest cyclotron

• This is at TRIUMF (CANARA)• Accelerates protons to energies up

to 520 MeV • Diameter of machine = 18 m• During the course of acceleration

proton travels 45 km

Magnetic Mirror• Non uniform magnetic field

Strong B Strong BWeak B

The Hall effect

• Provides a way to determine sign and density of charge carriers.

conductor w

If electrons are majority charge carriers

+ + + + + + + + + + + +

- - - - - - - - - - - - - - - -

EH

E

B

E

conductor

+ + + + + + + + + + + +

- - - - - - - - - - - - - - - -

VH

If the electrons are majority charge carriers

+

-conductor

0)( BvqEq dH

0 BvE dH

nqwt

IB

w

VE HH

Bnq

jBvE dH

nqwt

IBB

nq

jEH

Bnqwt

I

w

VE HH

BVqt

In

H

Density of charge carriers

Convention

• If the voltage of lower terminal is negative, electrons are the majority charge carriers.

• If the voltage of lower terminal is positive, holes are the majority charge carriers.

Show that , in terms of hall electric field EH, and the current density j, the number of charge carriers per unit volume is given by

HeE

jBn

Show that the ratio of hall electric field to the electric field

is given by

neB

E

E

C

H

jEc

Bne

jEH

A metal strip 10 cm long, 1 cm wide and 1mm thick moves with constant speed v through a magnetic field of 1mT perpendicular to the strip. A potential difference of 4 V is measured between the points x and y across the strip. Calculate the speed v

w

VBv Hd

Vd is the velocity of strip now

Vd = 0.4 m/s

A strip of copper 150 m thick is placed in a magnetic field B = 0.65 T perpendicular to the plane of the strip. A current 23 A is setup in the strip. What hall potential difference will appear across the width of the strip if there were 8.5 x 1028 electrons/m3 ?

BVet

In

H B

net

IVH

VVH 3.7