Magnetic field II. Plan Motion of charge particle in electric and magnetic fields Some applications...
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Transcript of Magnetic field II. Plan Motion of charge particle in electric and magnetic fields Some applications...
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