MHT CET · Physics · Electromagnetic Induction

A coil has an area \(0.06 \mathrm{~m}^2\) and it has 600 turns. After placing the coil in a magnetic field of strength \(5 \times 10^{-5} \mathrm{Wbm}^{-2}\), it is rotated through \(90^{\circ}\) in 0.2 second. The magnitude of average e.m.f induced in the coil is

A \(12 \times 10^{-3} \mathrm{~V}\)
B \(3 \mathrm{mV}\)
C \(3 \mathrm{~V}\)
D \(9 \times 10^{-3} \mathrm{~V}\)

Verified Solution

Answer & Solution

Correct Answer

(D) \(9 \times 10^{-3} \mathrm{~V}\)

Step-by-step Solution

Detailed explanation

Induced emf, \(\mathrm{e}=\frac{-\mathrm{N}\left(\phi_2-\phi_1\right)}{\mathrm{t}}=\frac{-\mathrm{NBA}\left(\cos \theta_2-\cos \theta_1\right)}{\mathrm{t}}\)
Assuming that the coil was initially placed perpendicular magnetic flux
\(
\begin{aligned}
& \theta_1=0^{\circ} \text { and } \theta_2=90^{\circ} . \\
& \mathrm{e}=\frac{-\mathrm{NBA}\left(\cos 90^{\circ}-\cos 0^{\circ}\right)}{\mathrm{t}} \\
& =\frac{-\mathrm{NBA}(0-1)}{\mathrm{t}}=\frac{\mathrm{NBA}}{\mathrm{t}} \\
& =\frac{600 \times 5 \times 10^{-5} \times 0.06}{0.2}=9 \times 10^{-3} \mathrm{~V}
\end{aligned}
\)

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.

Same subject

Explore more questions on app

From MHT CET

Explore more questions on app