Question

A conducting rod spans a gap of length L = 0.23 m and acts as the fourth side of a rectangular conducting loop, as shown in the figure. A constant magnetic field B = 0.55 T pointing into the paper is in the region. The rod is moving under an external force with an acceleration a = At², where A = 4.5 m/s⁴. The resistance in the wire is R = 145 Ω.

a. Express the magnitude of the magnetic flux going through the loop, Φ, in terms of B, x and L.

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

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

d. Express the derivative of the magnetic flux, dΦ/dt, in terms of B, A, L and t.

e. Express the magnitude of the emf induced in the loop, ε, in terms of B, L, A and t.

f. Express the current induced in the loop, I, in terms of ε and R.

g. Express the current induced in the loop, I, in terms of B, L, A, t, and R.

h. Calculate the numerical value of I at t = 2s in A.

Answer 1