A rectangular metallic loop having length l and width b is situated coplanar with a long wire carrying a current i (as shown in the figure). The loop travels perpendicular to the wire at a speed v within the plane containing both the wire and the loop. Determine the emf induced in the loop at the instant the rear end of the loop is at a distance a from the wire.

Step-by-step solution

The magnetic field produced by the long straight wire at a distance x is given by: B = ₀ i 2 x The loop is moving with velocity v perpendicular to the wire. The motional emf induced in a wire of length L moving in a perpendicular magnetic field is = B L v . For the horizontal sides of the loop (length l ), the velocity v is parallel to the length, so the induced emf is zero. For the left vertical side (length b ) which is at a distance a from the wire, the induced emf is: ₁ = B₁ b v = ₀ i 2 a b v For the right vert