A conducting rod of length L = 0309 m is lying on a rectangular wire as shown in the figure. A constant magnetic field B = 0.4 T pointing into the paper is in the region. The rod is moving under an external force with an acceleration a = At², where A =4 m/s⁴. The resistance in the wire is R = 15 Ω.

Part (a) Express the magnitude of the magnetic flux going through the loop, Phi, in terms of B, x and L.

Part (b) Express the speed of the rod, v, in terms of A and t. Assume y = 0 at t = 0.

Part (c) Express the position of the rod, x, in terms of A and t. Assume x = 0 at t = 0.

Part (d) Express the derivative of the magnetic flux, dphi/dt, in terms of B, A, L and t. d4/dt = -(BLA/3 ) t³.