W9_parallel_resonance.eps

Week 7: Sources of the Magnetic Field 253

Problem 7.

B field

Show that a uniform magnetic field that has no fringing field violates Ampere’s law. Use a
rectangular closed curveCthat lies partly inside, and partly outside, the region of confined field.
Then explain why this doesnotapply to the uniform field inside a solenoid, which goes “sharply”
to zero as one crosses thecurrentin the solenoid loops inside to outside.

Problem 8.

x

y

z

L

L

I

A square loop of wire lies in thex−yplane centered on thezaxis and carries a currentI. It
has side lengthL. Find the magnetic field at an arbitrary point on thezaxis, and show that in the
limitz≫Lit gives an expected result in terms of the magnetic momentmzof the loop.

Note that this problem is “simple” – just a repeated use of the field ofa straight segment of wire

• but visualizing thegeometryin terms of thegivensis not simple and is the object of the exercise.
  So draw a very good, very large picture! Or several! Visualize!