**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 current through the wire?

Solution:

Using one can solve
for * I*.

*I* = 195 amps (lots of 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 lower 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*

*
Examples
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