A coil of 50 turns has area 0.02 m² and is placed in a magnetic field of 0.5 T. The field makes an angle of 30° with the normal to the coil. If the magnetic field decreases at a rate of 0.02 T/s, what is the induced emf in the coil?

Step-by-step solution

1. Write the magnetic flux through the coil as (Phi = N B A cos\theta).
2. The rate of change of flux is (\frac{dPhi}{dt}=N Acos\theta,\frac{dB}{dt}).
3. Insert (N=50), (A=0.02;\text{m}^2), (cos30^circ = 0.866) and (\frac{dB}{dt}=-0.02;\text{T/s}).
4. Compute the magnitude: (50\times0.02=1,;1\times0.866=0.866,;0.866\times0.02=0.01732;\text{V}.

Concept tested: Faraday’s law with changing magnetic field

Published 4 September 2026 · Last updated 16 September 2026 · How this solution was prepared and checked