Physics 21
Fall, 2009
Solution to HW14
Cancelling Magnetic Field
Four
very
long,
current
carrying wires in the same plane intersect to form a square
with side lengths of 39.0 cm, as shown in the figure. The cur
rents running through the wires are 8.0 A, 20.0 A, 10.0 A,
and
I
.
Find the magnitude and direction of the current
I
that will make the magnetic field at the center of the square
equal to zero.
The field point at the center of the square is equidistant from
all four wires. Let this distance be
d
=
1
2
×
0
.
39 m. We just
have to keep track of the direction of each field using the
right hand rule. Let out of the page be plus, and let
I >
0
correspond to up:
B
out of page =
µ
0
2
πd
(
−
10 +
I
−
8 + 20)
Solving, we get
I
=
−
2 A, and the minus sign means
I
is
directed downward.
Wire and Square Loop
A square loop of wire with side
length
a
carries a current
I
1
. The center of the loop is located
a distance
d
from an infinite wire carrying a current
I
2
. The
infinite wire and loop are in the same plane; two sides of the
square loop are parallel to the wire and two are perpendicular
as shown. (a) What is the magnitude
F
of the net force on
the loop?
(b) The magnetic moment
μ
of a current loop
is defined as the vector whose magnitude equals the area of
the loop times the magnitude of the current ﬂowing in it
(
µ
=
IA
), and whose direction is perpendicular to the plane
in which the current ﬂows.
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 Spring '07
 Hickman
 Current, Force, Magnetic Field, Wire, Righthand rule, Bwire

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