Download t=0

Problem 2
Find the torque about the left hand
segment on the loop as a function of θ, the
angle the plane makes with the horizontal
plane.
Motion in magnetic field

1) Uniform B ,

2) Uniform B ,
3) Nonuniform
 
vB
 
vB

B
mv
r
qB
The angular velocity
v
v
qB
 

r mv
m
qB
Uniform magnetic field,
 
vB
Uniform
  
B, v  B
When a charged particle has velocity components both
perpendicular and parallel to a uniform magnetic field, the
particle moves in a helical path. The magnetic field does no
work on the particle, so its speed and kinetic energy remain
constant.
Example: A proton ( 1.60 1019 C, m  1.67 1027 kg) is
placed in the uniform magnetic field directed along the
x-axis with magnitude 0.500 T. Only the magnetic
force acts on the proton. At t=0 the proton has velocity
components
vx  1.50 105 m / s, v y  0, vz  2.00 105 m / s.
Find the radius of the helical path, the angular speed
of the proton, and the pitch of the helix (the distance
traveled along the helix axis per revolution).
Nonuniform

B.
A magnetic bottle.
mv
r
qB
The Magnetic Field
Current carrying wires
1820 Hans Christian Oersted
Hans Christian Ørsted
Biot-Savart Law
Infinitesimally small element of a current carrying wire produces an
infinitesimally small magnetic field

dS


 i ( ds  r )
dB 
3
r
i

r
  0 i (ds  r )
dB 
4
r3
0
is called permeability of free space
0  4 10 7 webers /( amp  meter)  4 10 7 N /( amp) 2
(Also called Ampere’s principle)
The Field Produced by a Straight Wire
0 i
B
2 a