First slide

Inductance

Question

A solenoid has 2000 turns wound over a length of 0.30 metre. The area of its cross-section is $1 .2 \times 10^{- 3} m^{2}$ . Around its central section, a coil of 300 turns is wound. If an initial current of 2 A in the solenoid is reversed in 0.25 sec, then the e.m.f. induced in the coil is

Moderate

A

$6 \times 10^{- 4} V$
B

$4 .8 \times 10^{- 3} V$
C

$6 \times 10^{- 2} V$
D

$48 mV$

Solution

$Induced emf e = M \frac{di}{dt} = \frac{μ_{0} N_{1} N_{2} A}{l} \cdot \frac{di}{dt}$
$\begin{array}{l} = \frac{4 π \times 10^{- 7} \times 2000 \times 300 \times 1.2 \times 10^{- 3}}{0.30} \times \frac{| 2 - (- 2) |}{0.25} \\ = 48.2 \times 10^{- 3} V = 48 mV \end{array}$

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