First slide

Magnetic flux and induced emf

Question

A coil with 1500 turns, a radius of 5.0 cm and a resistance of 12 $Ω$ 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 $π^{2} = 10$ , Neglect self inductance of the coil)

Moderate

Solution

$\begin{array}{l} ε = 1500 \times \frac{d}{dt} (μ_{0} ni) \times π \times {(\frac{4.0}{100})}^{2} \\ = 1500 \times 4 π \times 10^{- 7} \times \frac{250}{10^{- 2}} \times \frac{20}{0 .1} \times π \times \frac{4.0 \times 4.0}{10^{4}} \\ i = \frac{ε}{R} = \frac{6000 π^{2} \times 5000 \times 10^{3} \times 10^{- 7}}{12} \times \frac{(4.0)^{2}}{10^{4}} \\ i = 4 A \end{array}$

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