Physics 2212 – Summer GPS Week 5
Problem #1
A long wire is bent in the shape of a
rectangle with an extra half-loop protruding at right angles. The rectangular shape, which has dimensions of
L by w, is in the x-z plane; the halfloop, which has a radius R, is in the
x-y plane. A current I runs around the
wires as shown.
A. What is the direction of the magnetic field, due to the half-loop ONLY, at the origin?
B. What is the magnitude of the magnetic field, due to the half-loop ONLY, at the origin?
C. What is the direction of the magnetic field, due to the wire segment of length L ONLY, at the origin?
D. What is the net magnetic field (due to all wire segments including the half-loop) at the origin? Assume
w << L and neglect the field effects due to the straight line segments of length w.
E. Briefly describe how the net magnetic field at the origin would change if you had included the straight line
segments of length w
Problem #2
A bar magnet is centered on the origin and lies in the xy-plane as indicated in the diagram.
A. Sketch the direction of the magnetic field at the four locations marked with an “x”. Each location is the same
distance d from the center of the magnet. When sketching your arrows, pay attention to relative magnitude
of each arrow.
A coil of radius R << d with N loops of current I lies in the xz-plane. The center of the coil is located
on the x-axis a distance d from the origin as indicated in the diagram. The bar magnet is still located int
he xy-plane but the center of the magnet has been moved along the negative x-axis a distance d. At these
locations the magnetic field of the coil and bar magnetic exactly cancel at the origin.
B. Determine the direction of the current in the coil and briefly describe how you determined this.
C. Determine the magnetic dipole moment of the bar magnet µ in terms of the radius R, N , I of the coil.
D. Determine the net magnetic field at the origin if the bar magnet is rotated 90 degrees clockwise about it’s
center when viewed from the positive z-axis.
Problem #3
A proton and an electron move past each other with
the same speed v. As indicated in the diagram, the
velocities of the two particles are in the x and +x
directions respectively. At this moment in time, the
particles are separated by a distance d.
A. Determine the magnitude and direction of the net magnetic field at the midpoint between the two particles
(indicated by an “X” in the diagram).
B. Determine the magnitude and direction of the magnetic field due only to the proton a horizontal distance
d to the right of the proton (indicated by an * in the diagram).
C. Determine the magnitude and direction of the magnetic field due only to the electron a horizontal distance
d to the right of the proton (indicated by an * in the diagram)
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