Honors Physics II
Problem Set 6b (due Mon Apr 4)
Spring 2016
[In all assignments this semester, you are advised to first look at worked out examples
as well as work out simple problems from your textbook before you attempt the
homework problems assigned.]
1. Fig (a) shows a length of wire carrying a current i bent into a
circular coil of one turn. In Fig (b), the same length of wire has
been bent more sharply, to give a double loop of smaller radius.
(a) If Ba and Bb are the magnitudes of the magnetic fields at the
centers of the two loops, what is the ratio Bb/Ba?
(b) What is the ratio of their dipole moments µb/µa?
2. A wire-carrying current i has the configuration shown
in the figure. Two semi-infinite straight sections, each
tangent to the same circle, are connected by a circular arc,
of angle θ, along the circumference of the circle, with all
sections lying in the same plane. What must θ be in order
for the magnetic field B to be zero at the center of the
circle?
3. A long wire carries a current i1. The rectangular loop
carries a current i2. Calculate the resultant force acting
on the loop. Assume that a = 1.10 cm, b = 9.20 cm,
L = 32.2 cm, i1 = 28.6 A, and i2 = 21.8 A.
4. The figure shows a cross-section of a hollow cylindrical conductor
of radii a and b, carrying a uniformly distributed current i. (a) Using
the circular Amperian loop shown, verify that B(r) for the range
µ 0i
r 2 ! b2
b < r < a is given by B(r) =
2! (a 2 ! b 2 ) r
(a) Test this formula for the special cases of r = a, r = b, and b = 0.
(c) For a = 2.0 cm, b = 1.8 cm, and i = 100 A, plot B(r) for the range
0 < r < 6 cm.
5. A conductor consists of an infinite number of adjacent
wires, each infinitely long and carrying a current i0. Show,
by direct application of Ampere's Law, that the lines of B
are as represented in the figure, and that B for all points
above and below the infinite current sheet is given by
B(r) = 12 µ 0 ni0 , where n is the number of wires per unit
length.