**Examples
for magnetic fields and forces**

Example #1

Problem:

A current of 10.0
amps moves through a wire of diameter, * d *=
3.0

Solution:

The current in a wire is given by the charge per unit length times the velocity of the charge.

The charge per unit length is the charge per volume times the cross-sectional area of the wire.

One can then solve for the velocity using the first equation.

1.77E-3
*m/s*, pretty slow!

Example #2

Problem:

In the figure
below, the magnetic field has a strength of 0.75 *T*.
Three charged particles * a*,

Solution:

F_{a}
= 0, F_{b} = 1.5E-3 *N* , F_{c} = 7.5E-4 *N*

Example #3

Problem:

In the figure below, what are the net force and torque on the loop?

DATA: * I* = 3.0 amps,

Solution:

All the forces cancel out, but there is a force out of the screen from the right segment and a force into the screen on the left segment. These make the loop want to twist, and give it a torque:

F =
0, t = 1.575 *Nm*

Example #4

Problem:

An proton makes a
30 *cm* circular orbit in a 2.5 *T* magnetic field.
What is the velocity of the proton?

DATA: mass of
proton = 1.67E-27 *kg*, *e* = 1.602E-19 *C*.

Solution:

Use the relation:

to solve for the velocity.

* v*
= 7.2E7