Question

A physicist works in a laboratory where the magnetic field is 2 T. She wears a necklace enclosing area 0.01 m\(^2\) in such a way that the plane of the necklace is normal to the field and is having a resistance \(R = 0.01\ \Omega\). Because of power failure, the field decays to 1 T in time \(10^{-3}\) s. Then what is the total heat produced in her necklace?

• A. 10 J
• B. 20 J
• C. 30 J
• D. 40 J

Hint:

Heat equals energy dissipated in resistance due to induced current.

Answer 1

The Correct Option is A

Step 1: Understanding the Concept:
Induced emf \(E = -A \Delta B/\Delta t\), heat = \(E^2 t / R\).
Step 2: Detailed Explanation:
\(E = 0.01 \times (1 - 2)/10^{-3} = 10\ \mathrm{V}\)
\(H = (10^2 \times 10^{-3})/0.01 = 10\ \mathrm{J}\)
Step 3: Final Answer:
Heat produced is 10 J.