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

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 $s^{-1}$.