Question

circular coil consists of 100 turns and has a radius of 20 cm. It is placed in a region of space in which there is a magnetic field of 0.5 T. If the coil is initially perpendicular to the magnetic field, find the magnitude of the emf induced if in 0.2 sec:

a) the coil rotates 90 °

b) the coil rotates 180 °

c) The field is reduced to zero

Answer 1

Solution :

Given :

N = 100

r = 20 cm = 0.20 m

B = 0.5 T

θ = 0^o

Δt = 0.2 sec

Here, Initial magnetic flux through the coil will be :

Φ = B A cosθ = B (πr²) cosθ = (0.5 T)(π)(0.20 m)² cos(0) = 0.06283 Wb

.

Part (a) : When the coil rotates 90°

The final magnetic flux will be : Φ₂ = B A cos(90) = B (πr²) cos(90) = (0.5 T)(π)(0.20 m)² cos(90) = 0 Wb

Therefore : Induced emf : E = N (ΔΦ / Δt) = (100) { (0.06283 Wb) - (0 Wb) } / (0.2 sec) = 31.42 V

.

Part (b) : When the coil rotates 180°

The final magnetic flux will be : Φ₂ = B A cos(180) = B (πr²) cos(180) = (0.5 T)(π)(0.20 m)² cos(180) = - 0.06283 Wb

Therefore : Induced emf : E = N (ΔΦ / Δt) = (100) { (0.06283 Wb) - (- 0.06283 Wb) } / (0.2 sec) = 62.84 V

.

Part (c) : When the field is reduced to zero.

Then, The final magnetic flux will be : Φ₂ = B A cos(90) = B (πr²) cos(0) = (0 T)(π)(0.20 m)² cos(0) = 0 Wb

Therefore : Induced emf : E = N (ΔΦ / Δt) = (100) { (0.06283 Wb) - (0 Wb) } / (0.2 sec) = 31.42 V