Question

Consider a circular wire loop of radius R spinning about a diametrical chord which is perpendicular to a uniform magnetic field $(\vec{B}=B_0 \hat{k})$

• A. The magnitude of the induced EMF in the loop is maximum when the plane of the loop is perpendicular to $\vec{B}$
• B. Flux through the loop is minimum when the plane of the loop is perpendicular to $\vec{B}$
• C. The direction of induced current remains same during the spinning motion of the loop
• D. EMF induced will be the same for a larger radius of the loop in the same field
• E. No EMF will be induced since magnetic field is constant

Hint:

EMF depends on rate of change of flux, not just flux value.

Answer 1

The Correct Option is A

Concept:
\[ \Phi = BA\cos\theta,\quad \mathcal{E} = -\frac{d\Phi}{dt} \]

Step 1: Flux behavior.
Maximum change in flux when $\theta=90^\circ$.

Step 2: EMF condition.
EMF is maximum when rate of change of flux is maximum.

Step 3: Conclusion.
Occurs when loop plane is perpendicular to field.