W9_parallel_resonance.eps

Week 7: Sources of the Magnetic Field 251

Homework for Week 7

Problem 1.

Physics Concepts

Make this week’s physics concepts summary as you work all of the problems in this week’s
assignment. Be sure to cross-reference each concept in the summary to the problem(s) they were
key to. Do the work carefully enough that you can (after it has been handed in and graded) punch
it and add it to a three ring binder for review and study come finals!

Problem 2.

I

I

1

2

d

b

a

An infinitely long straight wire carries a currentI 1 in the +zdirection. Atx=dthere is a
rectangular loop of currentI 2 in thex−zplane, with two sides of lengthaparallel to the long wire
and two sides of lengthbperpendicular to the long wire. The current in the wire segment nearest
the long wire isparallelto the currentI 1 in the +zdirection. Find the net force acting on the
rectangular loop.

Problem 3.

Using Ampere’s Law, find the magnetic field in all space produced by:

a) A solid conducting cylinder carrying a total currentI.

b) Two cylindrical conductings shells carrying opposite currents (each equal toIin magnitude).

The inner one has radiusa, the outer oneb.

c) A solenoid withNturns and lengthLcarrying currentIin each turn (inside only, far from

the ends).

d) A toroidal solenoid withNturns, inner radiusa, outer radiusb.

e) An infinite plane sheet of current into the paper (above and belowthe sheet).

This more or less exhausts thekindsof possible problems where one can find the magnetic field using
Ampere’s Law. Most were examples in lecture, so this forces you to recapitulate on your own what
you saw presented there.