PHYS 1404-004 Homework 7 – 04/07/2016
Due April 14th, 2016
Homework should be written out neatly on a separate sheet of paper. Explain your
reasoning.
1. Consider the four cubes shown below, numbered 1 through 4. Three of the faces of each
cube are labeled A, B, C.
•
•
•
surface 2B attracts surface 4A
surface 1A attracts surface 4C
surface 3B does not interact with 1A
Determine if each of the cubes is a magnet, a ferromagnet or non-magnetic. Explain. If
you cannot determine which class a cube belongs to, explain why you cannot.
2. The strength of the magnetic field created by a current-carrying wire found
experimentally is
B=
µ0 I
2πr
where r is the distance from the wire, I is the current, and µ0 = 4 π × 10-7 Tm/A is a
constant.
Two wires lie perpendicular to the plane of the paper and carry equal magnitude of
electric current in the directions shown. Point P is equidistant from the two wires. The
distance between each of wires and the distance of point P from each of the wires is
3.00cm, as shown in the diagram, and the magnitude of the current through each of the
two wires is 2.00A.
a. Determine the magnitude and direction of the net magnetic field at point P.
Explain your reasoning.
b. Suppose a third wire of length 1.5m, carrying an equal amount of current
(2.00A) into the plane of the paper were located at P. What would be the
magnitude and direction of the force on the third wire? Explain your reasoning.
3. A horseshoe magnet, with its north and south poles indicated, is shown in the figure
below. Between the poles of the magnet is a wire perpendicular to the page, with
current out of the page.
a. Draw magnetic field lines for the magnet. Explain why you drew the field lines
the way you did.
b. If there is a force acting on the wire, indicate the direction of the force in the
diagram. Explain why there is or is not a force and how you determined the
direction of the force.
c. Does the magnet experience a force? If so, in which direction? If the magnet
does experience a force, explain why it experiences a force. If the magnet does
not experience a force, explain why it does not experience a force.
4. In the diagram below, in the region inside the circle, a magnetic field is directed into the
paper. The magnitude of the magnetic field is increasing in time.
Rank the brightness of the bulbs in the following cases:
a. when both switches are open. Explain your reasoning.
b. when switch S1 is open and switch S2 is closed. Explain your reasoning.
c. when both switches are closed and bulb B is removed (unscrewed) from the
circuit. Explain your reasoning.
5. Consider a U-shaped metal rod with a metal rod touching it, which is free to slide
(shown below). A magnetic field is out of the page everywhere, as in the diagram below.
If the rod is moving to the right at a velocity v,
a. would there be a current? Explain. If so, determine the direction of the current.
b. would there be an emf? Explain. If so, calculate the emf in terms of the
magnetic field, B, the velocity of the rod, v, and the length l.
6. Consider the following situation shown below. A mass, m = 2.4kg, is hung from a
conducting wire shaped into a loop. The dimensions of the loop are 2m x 1.8m. Part of
the loop is in a region where the magnetic field (B = 1.4T) is into the page everywhere.
If there were a current in the wire loop,
a. which direction would the current have to flow in order for the wire to be at
rest and not fall? Show your work and explain your reasoning.
b. what would the magnitude of the current have to be in order for the wire to be
at rest and not fall? Show your work and explain your reasoning.