Question

A circular ciol, of average radius R, having N turns and carrying a current I, is set-up, horizontally with its plane in the x–y plane and its axis along the z–axis, so shown. A small rectangular lamina of sides Δa and Δb , is set up with its centre on the z–axis and its plane parallel to the xy plane. If this lamina is flipped over through an angle π, in time Δt , the magnitude of the emf, momentairly induced, in it, would equal (nearly)

(1) zero

(2) \(\frac{(Δa)(Δb)}{Δt}N\frac{μ_0I}{(R)}\)

(3) \(\frac{(Δa)(Δb)}{Δt}N\frac{μ_0R^2I}{(R^2+z^2)^{3/2}}\)

(4) \(\frac{(I)(Δa)(Δb)}{2Δt}N\frac{μ_0R^2I}{(R^2+z^2)^{3/2}}\)

Answer 1

 (3) \(\frac{(Δa)(Δb)}{Δt}N\frac{μ_0R^2I}{(R^2+z^2)^{3/2}}\)

The magnetic field, due to the current carrying circular coil, at the centre of the rectangular lamina

The field can be assumed to have this (nearly) constant magnitude all over the plane of the small lamina. Hence the change in flux through it, when it is ‘flipped over’ is

∴ Magnitude of emf induced