Question:
A coil having effective area 'A' is held with its plane normal to a magnetic field of induction 'B'. The magnetic induction is quickly reduced to \(25\%\) of its initial value in \(2\) second. Then e.m.f. induced across the coil will be
A coil having effective area 'A' is held with its plane normal to a magnetic field of induction 'B'. The magnetic induction is quickly reduced to \(25\%\) of its initial value in \(2\) second. Then e.m.f. induced across the coil will be
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Use Faraday's law with the change in flux over the time interval.
Updated On: Nov 12, 2026
- \(\frac{AB}{2}\)
- \(\frac{AB}{4}\)
- \(\frac{3AB}{4}\)
- \(\frac{3AB}{8}\)
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The Correct Option is D
Solution and Explanation
Step 1: Understanding the Concept
Induced emf is \(e=\dfrac{\Delta\Phi}{\Delta t}\) with \(\Phi=BA\) for a plane normal to the field.
Step 2: Change in flux
Final field is \(0.25B\), so \(\Delta\Phi=A(B-0.25B)=0.75AB\).
Step 3: Calculation
\(e=\dfrac{0.75AB}{2}=\dfrac{3AB}{8}\).
Final Answer:
The induced emf is 3AB divided by 8. \[ \boxed{\text{(D) }\dfrac{3AB}{8}} \]
Induced emf is \(e=\dfrac{\Delta\Phi}{\Delta t}\) with \(\Phi=BA\) for a plane normal to the field.
Step 2: Change in flux
Final field is \(0.25B\), so \(\Delta\Phi=A(B-0.25B)=0.75AB\).
Step 3: Calculation
\(e=\dfrac{0.75AB}{2}=\dfrac{3AB}{8}\).
Final Answer:
The induced emf is 3AB divided by 8. \[ \boxed{\text{(D) }\dfrac{3AB}{8}} \]
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