Question:
A rectangular loop of area \(A\) lies in a uniform magnetic field \(B\) with its plane perpendicular to the field. If the loop rotates through \(90^\circ\) in time \(T/4\), then the induced emf during this interval is:
A rectangular loop of area \(A\) lies in a uniform magnetic field \(B\) with its plane perpendicular to the field. If the loop rotates through \(90^\circ\) in time \(T/4\), then the induced emf during this interval is:
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Use Faraday’s law: induced emf depends on rate of change of magnetic flux.
Updated On: Jun 19, 2026
- 0
- \(\frac{2BA}{T}\)
- \(\frac{4BA}{T}\)
- \(\frac{6BA}{T}\)
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The Correct Option is C
Solution and Explanation
Step 1: Initial magnetic flux.
Initially plane is perpendicular to field, so normal is parallel to \(B\): \[ \Phi_i = BA \]
Step 2: Final magnetic flux.
After rotation by \(90^\circ\), plane becomes parallel to field: \[ \Phi_f = 0 \]
Step 3: Change in flux.
\[ \Delta \Phi = BA \]
Step 4: Time interval.
\[ \Delta t = \frac{T}{4} \]
Step 5: Induced emf.
\[ \mathcal{E} = \frac{\Delta \Phi}{\Delta t} = \frac{BA}{T/4} \]
Step 6: Final result.
\[ \mathcal{E} = \frac{4BA}{T} \]
Final Answer: \[ \boxed{\frac{4BA}{T}} \]
Initially plane is perpendicular to field, so normal is parallel to \(B\): \[ \Phi_i = BA \]
Step 2: Final magnetic flux.
After rotation by \(90^\circ\), plane becomes parallel to field: \[ \Phi_f = 0 \]
Step 3: Change in flux.
\[ \Delta \Phi = BA \]
Step 4: Time interval.
\[ \Delta t = \frac{T}{4} \]
Step 5: Induced emf.
\[ \mathcal{E} = \frac{\Delta \Phi}{\Delta t} = \frac{BA}{T/4} \]
Step 6: Final result.
\[ \mathcal{E} = \frac{4BA}{T} \]
Final Answer: \[ \boxed{\frac{4BA}{T}} \]
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