CHAPTER 28:
Sources of Magnetic Field
Responses to Questions
1. Alternating currents will have little effect on the compass needle, due to the rapid change of
the direction of the current and of the magnetic field surrounding it. Direct currents will
deflect a compass needle. The deflection depends on the magnitude and direction of the
current and the distance from the current to the compass. The effect on the compass
decreases with increasing distance from the wire.
2.
The magnetic field due to a long straight current is proportional to the current strength. The
electric field due to a long straight line of electric charge at rest is proportional to the charge
per unit length. Both fields are inversely proportional to the distance from the wire or line of
charge. The magnetic field lines form concentric circles around the wire; the electric field
lines are directed radially outward if the line of charge is positive and radially inward if the
line of charge is negative.
3.
The magnetic forces exerted on one wire by the other try to align the wires. The net force on
either wire is zero, but the net torque is not zero.
4.
Yes. Assume the upper wire is fixed in position. Since the currents in the wires are in the
same direction, the wires will attract each other. The lower wire will be held in equilibrium
if this force of attraction (upward) is equal in magnitude to the weight of the wire
(downward).
5.
(
a
) The current in the lower wire is opposite in direction to the current in the upper wire.
(
b
) The upper wire can be held in equilibrium due to the balance between the magnetic
force from the lower wire and the gravitational force. The equilibrium will be stable for
small vertical displacements, but not for horizontal displacements.
6.
(
a
) Let
21
.
II
=
()
0e
n
c
l
0
1
2
01
2
dI
I
I
I
µµ
µ
⋅=
=
+ =
∫
B
l
r
r
(
b
) Let
.
=−
n
c
l
0
1
2
0
I
I
=
∫
B
l
r
r
Inside the cavity
since the geometry is cylindrical and no current is enclosed.
0
=
B
r
8.
Construct a closed path similar to that shown in part (
a
) of the figure, such that sides
ab
and
cd
are perpendicular to the field lines and sides
bc
and
da
lie along the field lines. Unlike
part (
a
), the path will not form a rectangle; the sides
ab
and
cd
will flare outward so that side
bc
is longer than side
da
. Since the field is stronger in the region of
da
than it is in the region
of
bc
, but
da
is shorter than
bc
, the contributions to the integral in Ampère’s law may cancel.
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 Spring '09
 Thomas
 Current, Magnetic Field

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