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A physicist works in a laboratory where the magnetic field is 2 T. She wears a necklace enclosing area 0.01 m² in such a way that the plane of the necklace is normal to the field and is having a resistance R = 0.01 Ω. Because of power failure, the field decays to 1 T in time 10^–3 seconds. Then what is the total heat produced in her necklace? (T = Tesla)

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30 J

40 J

10 J

20 J

answer is A.

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Detailed Solution

Heat produced in the necklace (worked solution)

Given:

Initial magnetic field, B₁ = 2 T
Final magnetic field, B₂ = 1 T
Area of loop, A = 0.01 m²
Resistance of necklace, R = 0.01 Ω
Time of change, Δt = 10⁻³ s

Step 1 — Change in magnetic flux (ΔΦ):

ΔΦ = A × (B₁ − B₂)

ΔΦ = 0.01 × (2 − 1) = 0.01 Wb

Step 2 — Induced emf (Faraday's law):

ε = ΔΦ / Δt

ε = 0.01 / 10⁻³ = 10 V

Step 3 — Induced current:

I = ε / R = 10 / 0.01 = 1000 A

Step 4 — Heat produced (Joule heating):

H = I² R Δt

H = (1000)² × 0.01 × 10−3 = 10 J

Final answer: Heat produced = 10 J

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