MASSACHUSETTS INSTITUTE OF TECHNOLOGY
Department of Physics
8.02
Fall 2007
Turn in at your table during class labeled with your name and group (e.g. L02 3C)
Problem Set 7
Due: Wednesday, October 24
th
at beginning of class (before 10:15/1:15)
This problem set focuses on material from classes 15-17 (week 7).
Textbook references
can be found at the top of the summaries from these three days.
Warm Up
Problem 1:
Quickies…
a)
Two semicircular arcs have radii
R
2
and
R
1
, carry current
i
,
and share the same center of curvature C.
What is the
magnitude of the net magnetic field at C?
b)
A wire with current
i
is shown at left. Two semi-infinite
straight sections, both tangent to the same circle with radius
R
, are connected by a circular arc that has a central angle
θ
and runs along the circumference of the circle. The
connecting arc and the two straight sections all lie in the
same plane. If
B
= 0 at the center of the circle, what is
θ
?
c)
The figure at left shows two closed paths wrapped around
two conducting loops carrying currents
i
1
and
i
2
. What is the
value of the integral
d
⋅
∫
B
s
G
G
v
for
(a)
path 1 and
(b)
path 2?
ction.
Problem 2:
Two Currents
In the figure at left a long circular pipe with outside radius
R
carries a
(uniformly distributed) current
i
into the page. A wire runs parallel to
the pipe at a distance of 3.00
R
from center to center. Find the current
in the wire such that the ratio of the magnitude of the net magnetic
field at point
P
to the magnitude of the net magnetic field at the
center of the pipe is
x
, but it has the opposite dire
PS07-1

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