A 23-turn circular coil of wire has diameter 0.93 m. It is placed with its axis along the direction of the Earth's magnetic field of 58.0 µT and then in 0.200 s is flipped 180°. An average emf of what magnitude is generated in the coil?

9.058 mV

Explanation:

N = 23, Diameter = 0.93 m, radius, r = 0.465 m, B = 58 x 10^-6 T

Area, A = 3.14 x (0.465) ^2 = 0.679 m^2

θ1 = 0 degree, θ2 = 180 degree, t = 0.2 s

According to the Faraday's law of electromagnetic induction, the induced emf is equal to the rate of change of magnetic flux.

e = - dΦ / dt

where, negative sign gives the direction of induced emf.

Φ1 = N B A Cosθ1 = 23 x 58 x 10^-6 x 0.679 x Cos 0 = 9.057 x 10^-4 Weber

Φ2 = N B A Cosθ2 = 23 x 58 x 10^-6 x 0.679 x Cos 180

= - 9.057 x 10^-4 Weber

So, change in flux, dΦ = Φ2 - Φ1 = - 9.057 x 10^-4 - 9.057 x 10^-4

= - 1.81 x 10^-3 Weber

So, induced emf, e = 1.81 x 10^-3 / 0.22 = 9.058 x 10^-3 V = 9.058 mV