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IV. [25 points total]
A. A bar magnet is shown in cross-section at right. Points A
and B are equidistant from the ends of the bar magnet.
[5 pts] Indicate the direction of the magnetic field at points A
and B. If the magnetic field is zero at either point, state that explicitly.
B. A second bar magnet, identical to the first,
is placed as shown in the diagram at right.
i.
[5 pts] Does the magnitude of the magnetic field at point A increase, decrease, or remain the
same? Explain.
Magnetic fields obey the superposition principle, so the new magnetic field at each point will be the sum
of the contributions from each bar magnet. The new magnet will contribute a magnetic field at point A
which points to the left (into its south pole). This is in the same direction as the original magnetic field
at point A, so the magnitude will increase.
ii. [5 pts] Does the magnitude of the magnetic field at point B increase, decrease, or remain the
same? Explain.
The new magnet will contribute magnetic field directed to the left. Since the original field at point B
pointed left, the magnitude of the magnetic field at point B will increase.
iii. [5 pts] With the second bar magnet in place, is the magnitude of the magnetic field at point A
greater than, less than, or equal to that at point B? Explain.
Magnetic field lines from a bar magnet tend to spread out as one moves away from the poles of the
magnet, so the strength of the field drops off with distance. Points A and B were equidistant from the
original bar magnet, so the magnitude of the magnetic at each point was initially the same. Since the
new magnet is closer to point A than point B, the magnetic field at point A will be increased by a larger
amount than the magnetic field at point B. Thus, the magnitude of the net magnetic field at point A will
be greater than that at point B.
C. [5 pts] A triangular loop of wire carrying a current io = 5A in the
direction shown is placed near an infinite wire carrying a current io = 5A
in the direction shown. On the diagram, indicate the direction of the net
force exerted on the loop by the wire. If the net force is zero, state so
explicitly. Explain.
The leg of the triangle closest to the straight wire will feel a repulsive force
directed straight down the page. The other legs of the triangle will each feel
a force perpendicular to the leg and directed up. The horizontal components
of these forces will add to zero by symmetry. The vertical components will add, but the total magnitude
of the forces on these wires is reduced because the strength of the magnetic field of the straight wire
decreases as one moves along the length these wires. Thus, the net force is in the downward direction.
Physics 122B, Autumn 2005
Final Exam
13 December 2005
EM-UWA122B054T-FE(MMF)