A conducting loop of finite resistance R lies in the xy-plane in a uniform time-independent magnetic field B along z. Its area changes with time according to A(t) = A₀(1 + sin t). Which curve best represents power P dissipated as a function of t? Image (four power–time graphs)
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Question

A conducting loop of finite resistance R lies in the xy-plane in a uniform time-independent magnetic field B along z. Its area changes with time according to A(t) = A₀(1 + sin t). Which curve best represents power P dissipated as a function of t? Image (four power–time graphs)

Options

G1 Physics · Accepted Answer

Step 1: Magnetic flux is Φ(t) = BA(t) = BA₀(1 + sin t). Step 2: Faraday's law gives magnitude of induced emf |ε| = |dΦ/dt| = BA₀|cos t|, with the time scale expressed in the problem's units. Step 3: Dissipated electrical power in the resistive loop is P = ε²/R. Step 4: Hence P(t) = (B²A₀²/R)cos²t. Step 5: At t = 0 the power is maximal; at t = π/2 it becomes zero, and then rises again. Final answer: Graph 2 (Option B).