Let the wire loop of Problem 9.4 be stationary in its t = 0 position and find the induced emf that results from a magnetic flux density given by B(y, t) = B₀ cos(ωt − βy) a_z, where ω and β are constants.

In Problem

A rectangular loop of wire containing a high-resistance voltmeter has corners initially at (a/2, b/2, 0), (−a/2, b/2, 0), (−a/2,−b/2, 0), and (a/2,−b/2, 0). The loop begins to rotate about the x axis at constant angular velocity ω, with the first-named corner moving in the a_z direction at t = 0. Assume a uniform magnetic flux density B = B₀a_z. Determine the induced emf in the rotating loop and specify the direction of the current.