A circular loop of radius 0.15 m rotates with constant angular speed 120 rad/s in a uniform magnetic field of 0.2 T that is perpendicular to the plane of the loop. Derive the expression for the instantaneous induced emf and compute its maximum value.

Step-by-step solution

1. Write the magnetic flux through the loop as (Phi(t)=B,A,cos(\theta)) where (A=pi R^2) and (\theta=omega t).
2. Compute the area: (A=pi(0.15)^2=0.0707;\text{m}^2.)
3. Express the flux: (Phi(t)=0.2\times0.0707cos(120t).)
4. The induced emf is (varepsilon = -\frac{dPhi}{dt}=B,A,omega,sin(omega t).)
5. Substitute the numerical values: (varepsilon = 0.2\times0.0707\times120sin(120t).)
6. The maximum value occurs when (sin(120t)=1), giving (${\epsilon }_{\text{max}}$ = 0.2\times0.0707\times120 = 1.695;\text{V} approx 1.70;\text{V}.

Concept tested: Induced emf in rotating loop

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