A conducting circular loop of area 1.0 m² is placed perpendicular to a magnetic field which varies as B = sin(100 t) Tesla. If the resistance of the loop is 100 Ω, then the average thermal energy dissipated in the loop in one period i $s ______J.$
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Question

A conducting circular loop of area 1.0 m² is placed perpendicular to a magnetic field which varies as B = sin(100 t) Tesla. If the resistance of the loop is 100 Ω, then the average thermal energy dissipated in the loop in one period i $s ______J.$

Options

G1 Physics · Accepted Answer

The magnetic flux through the loop is Φ = BA. Since A = 1.0 m², Φ = sin(100t). The induced emf magnitude is ε = | dΦ /dt| = 100|cos(100t)|. The instantaneous power dissipated is P = ε² /R = 10000 cos²(100t) / 100 = 100 cos²(100t). The time period of the magnetic field is T = 2π / 100 s = π /50 s. The thermal energy dissipated in one complete period is Q = ∫P dt over one complete period. The average value of cos² over one period is ½. Therefore, Q = 100 × ½ × T = 50 × π/50 = π J. Correct option:…

A conducting circular loop of area 1.0 m² is placed perpendicular to a magnetic field which varies as B = sin(100 t) Tesla. If the resistance of the loop is 100 Ω, then the average thermal energy dissipated in the loop in one period i s ______J.