AP Physics C E and M 12.3: Current-Carrying Wires

E\&M.3.
A conducting bar of mass M, length L, and negligible resistance is connected to two long vertical conducting rails of negligible resistance. The two rails are connected by a resistor of resistance R at the top. The entire apparatus is located in a magnetic field of magnitude B directed into the page, as shown in the figure above. The bar is released from rest and slides without friction down the rails.

Is the magnitude of the net magnetic field above the bar at point C greater than, less than, or equal to the magnitude of the net magnetic field before the bar is released? Greater than Less than Equal to
Justify your answer.

While the bar is above point D, is the magnitude of the net magnetic field at point D greater than, less than, or equal to the magnitude of the net magnetic field before the bar is released? Greater than Less than Equal to
Justify your answer.

Express your answers to parts (c) and (d) in terms of M, L, R, B, and physical constants, as appropriate.

The figures above represent different views of two long, straight, horizontal wires, 1 and 2, carrying currents $I_{1}=I$ and $I_{2}=2 I$, respectively, in the directions shown. The wires are held in place. In Figure 1, the current in wire 1 is directed out of the page, and wire 1 is a distance d above wire 2. Point P is a horizontal distance d from wire 1 and a distance d directly above wire 2. Express your answers to parts (a) and (b) in terms of I, d, and physical constants, as appropriate.

Wire 1 is now released. Which of the following best describes the initial motion of wire 1 due to the magnetic field of wire 2 ? Assume gravitational effects are negligible.

Wire 1 will not move. Wire 1 will move upward as viewed in Figure 1. Wire 1 will move downward as viewed in Figure 1. Wire 1 will rotate clockwise as viewed in Figure 2. Wire 1 will rotate counterclockwise as viewed in Figure 2.

Justify your answer.

Wire 1 is now replaced by a conducting rectangular loop of length $\ell$, width w, and resistance R. The loop is placed a distance d from wire 2, as shown. The loop, wire, and distance d are all in the plane of the page. The long side of the loop is parallel to the wire. The current $I_{2}$ for wire 2 is decreasing linearly as a function of time t according to the equation $I_{2}=2 I_{0}(1-k t)$, where k is a positive constant with units of $s^{-1}$.