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Question:

A conducting circular loop made of a thin wire, has area 3.5 × 10⁻⁷ m² and resistance 10 Ω. It is placed perpendicular to a time-dependent magnetic field B(t) = (0.4T)sin(50πt). The field is uniform in space. Then the net charge flowing through the loop during t = 0s and t = 10ms is close to:

0.21mC

7mC

0.14mC

6mC

Solution:

Q = ΔΦ/R = (1/R)∫E.dt = (1/R)∫(-dΦ/dt)dt = (1/R)(Φi - Φf) = (1/R)A(Bf - Bi) = (1/10) × 3.5 × 10⁻⁷ × (0.4sin(50π × 0.01) - 0.4sin(0)) = (1/10) × 3.5 × 10⁻⁷ × (0.4sin(π/2)) = 1.4 × 10⁻⁸ C = 0.14mC