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

Bv

2) Uniform , B

Bv

3) Nonuniform B

qB

mvr

The angular velocity

m

qB

qBmvv

r

v

Uniform magnetic field, Bv

Uniform , B

Bv

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 ( ) 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 componentsFind 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).

kgmC 2719 1067.1,1060.1

./1000.2,0,/1050.1 55 smvvsmv zyx

Nonuniform .B

A magnetic bottle.

qB

mvr

The Magnetic Field

Current carrying wires1820 Hans Christian Oersted

Hans Christian Ørsted

Biot-Savart Law

3

)(

r

rsdiBd

Infinitesimally small element of a current carrying wire produces an infinitesimally small magnetic field

Sd

i

(Also called Ampere’s principle)

30 )(

4 r

rsdiBd

r

0 is called permeability of free space

2770 )/(104)/(104 ampNmeterampwebers

The Field Produced by a Straight Wire

a

iB

2

0