**Examples
for Magnetic field sources**

Example #1

Problem:

A magnetic field
of magnitude 1.30E-3 *T* is measured a distance of 3.0 *cm*
from a long straight wire. What is the magnetic field of the
wire?

Solution:

Using one can solve for * I*.

*I* = 195 amps, quite a
current!

Example #2

Problem:

a.) Two wires carry currents in the same direction as shown below. Where are the points where the magnetic field is zero?

Solution:

Using the right-hand rule, will
convince one that the magnetic field contriubtions from the two
wires only cancel in the region between the wires. One must find
a position that is four times closer to the upper wire, which
would be one *cm* below the upper wire. Using algebra to
come to the same conclustion, consider a point located a distance
* y* below the upper wire.

Solving for * y*
gives the 1.0

1.0
*cm* below the upper wire

b.) Now consider
two wires carrying currents in the **opposite**
direction as shown below. Where are the points where the magnetic
field is zero?

Solution:

Using the right-hand rule again,
allows one to see that the magnetic-field contributions from the
two wires have opposite signs either above or below the wires,
but not between them. Of course when you are below the lowere
wire, the upper wire can never cancel out the lower wire's
contribution since the lower wire carries more current and is
closer to you. Therefore consider a point a distance * y*
above the upper wire.

Solving for * y*,

1.67
*cm* above the upper wire

Example #3

Problem:

What is the force felt by the square loop shown below due to the current in the long wire?

Solution:

There is no net contribution from
the two vertical segments of the rectangular loop since the
currents are in opposite directions. Using with * r*
= 2.0

* F*
= 1.71E-6

Example #4

Problem:

A long cylindrical
solenoid with 200 turns/*cm* carries a current of 4.0
amps. The diameter of the solenoid is 0.4 *cm* and the
length is 8.0 *cm* and the mass of the moon is 7.35E22 *kg*.
What is the magnetic field inside the solenoid?

Solution:

The magnetic field only depends on
the current (* I* = 4.0 amps) and the number of turns per
unit length (

B
=0.1005 *T*