Question

A coil of effective area \(3\) m\(^2\) is placed at right angles to a magnetic field of induction \(0.05\) Wb/m\(^2\). If the field is decreased to \(20\%\) of its original value in \(10\) second, the e.m.f. induced in the coil will be

• A. \(15\) mV
• B. \(12\) mV
• C. \(10\) mV
• D. \(5\) mV

Hint:

emf = A times change in B divided by time.

Answer 1

The Correct Option is B

Step 1: Understanding the Concept:
By Faraday's law, the induced emf is \(|\varepsilon| = \frac{\Delta\Phi}{\Delta t}\). With the coil perpendicular to the field, \(\Phi = BA\).

Step 2: Compute the change:
Initial \(B = 0.05\) Wb/m\(^2\). Final \(B = 0.2\times0.05 = 0.01\) Wb/m\(^2\). So \(\Delta B = 0.04\) Wb/m\(^2\).

Step 3: Find the emf:
\[ \varepsilon = \frac{A\,\Delta B}{\Delta t} = \frac{3\times0.04}{10} = 0.012\text{ V} = 12\text{ mV} \]

Step 4: Why the other options are wrong.
15 mV would come from \(\Delta B = 0.05\) (field dropping to zero). 10 mV and 5 mV do not match the area and field change.

Final Answer:
The induced emf is \(12\) mV, option (B). \[ \boxed{12\text{ mV}} \]