AP Free Response Question 2008 C3 E&M

The circular loop of wire in Figure 1 above has a radius of R and carries a current I. Point P is a distance of R2 above the center of the loop. Express algebraic answers to parts (a) and (b) in terms of R, I, and fundamental constants.

 (a) i. State the direction of the magnetic field B1 at point P due to the current in the loop.

 (a) ii. Calculate the magnitude of the magnetic field B1 at point P.

A second identical loop also carrying a current I is added at a distance of R above the first loop, as shown in Figure 2 above.

 (b) Determine the magnitude of the net magnetic field Bnet at point P.

A small square loop of wire in which each side has a length s is now placed at point P with its plane parallel to the plane of each loop, as shown in Figure 3 above. For parts (c) and (d), assume that the magnetic field between the two circular loops is uniform in the region of the square loop and has magnitude Bnet.

 (c) In terms of Bnet and s, determine the magnetic flux through the square loop.

 (d) The square loop is now rotated about an axis in its plane at an angular speed ω. In terms of Bnet, s, and ω, calculate the induced emf in the loop as a function of time t, assuming that the loop is horizontal at t = 0.