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JEE Main202226 Jul 2022Evening ShiftPhysicsElectromagnetic InductionActual

In a coil of resistance 8 Ω , the magnetic flux due to an external magnetic field varies with time as ϕ = 2 3 9 - t 2 . The value of total heat produced in the coil, till the flux becomes zero, will be _____ J .

Correct answer

0

Step-by-step solution

It is given that magnetic flux ϕ = 2 3 9 - t 2 For magnetic flux to be zero 0 = 2 3 9 - t 2 ⇒ t = 3   s According to Faraday's law of electromagnetic induction, ε = - d ϕ d t = - 2 3 0 - 2 t = 4 t 3 Heat produced from 0 to 3   s , H = ∫ 0 3 ε 2 R d t = ∫ 0 3 16 t 2 9 × 8 d t = 2   J

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