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Question

A coil with 1500 turns, a radius of 5.0 cm and a resistance of 12$\mathrm{\Omega}$ surrounds a solenoid with 250 turns/cm and a radius of 4 cm; see figure. The current in the solenoid changes at a constant rate from 0 to 20 A in 0.10 s. The magnitude of the induced current (in A) in the 1500 turn coil is ( Take ${\pi}^{2}=10$, Neglect self inductance of the coil)

Moderate

Solution

$\begin{array}{l}\mathrm{\epsilon}=1500\times \frac{\mathrm{d}}{\mathrm{dt}}\left({\mathrm{\mu}}_{0}\mathrm{ni}\right)\times \pi \times {\left(\frac{4.0}{100}\right)}^{2}\\ =1500\times 4\mathrm{\pi}\times {10}^{-7}\times \frac{250}{{10}^{-2}}\times \frac{20}{0.1}\times \mathrm{\pi}\times \frac{4.0\times 4.0}{{10}^{4}}\\ \mathrm{i}=\frac{\mathrm{\epsilon}}{R}=\frac{6000{\mathrm{\pi}}^{2}\times 5000\times {10}^{3}\times {10}^{-7}}{12}\times \frac{(4.0{)}^{2}}{{10}^{4}}\\ i=4\mathrm{A}\\ \end{array}$

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