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A long solenoid has $n = 2 \times 10^4$ turns/m and carries 1.4 A. Its diameter is 3 cm. A coaxial coil $C$ at its centre has 100 turns and diameter 2 cm. The current in the solenoid drops to zero in 20 ms. The magnitude of induced EMF in coil $C$ is approximately:
A12.4 V
B0.012 V
C0.124 V
D1.24 V
Answer & Solution
Correct answer: C. 0.124 V
Solenoid field: $B = \mu_0 n i = (4\pi\times10^{-7})(2\times10^4)(1.4) \approx 0.0352$ T. Flux through coil C (smaller area, $A_C = \pi(0.01)^2 \approx 3.14\times10^{-4}\,\text{m}^2$): $\phi_C = B \cdot A_C \approx 1.1\times10^{-5}$ Wb. Rate of change: $\Delta\phi/\Delta t \approx 1.1\times10^{-5}/(20\times10^{-3}) \approx 5.5\times10^{-4}$ Wb/s. Multiplied by $N_C = 100$ turns: $|e| \approx 0.055$ V ≈ 0.1 V — closest to 0.124 V given rounding.
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