Question

What is the emf induced in the coil when the current through the solenoid is decreasing at a rate $-0.20A/s$?

• A. $3.14\times {10}^{-6}V$
• B. $7.14\times {10}^{-5}V$
• C. $2.14\times {10}^{-7}V$
• D. $5.14\times {10}^{-5}V$

Answer 1

The correct option is A $3.14\times {10}^{-6}V$

In the theory we have already derived mutual inductance between solenoid and coil,

$M=\frac{{\mu }_0{N}_1{N}_2\left(\pi R_1^2\right)}{l_1}=\frac{{\mu }_0{N}_1{N}_2{S}_1}{l_1}$

$\left|e_2\right|=\left|M\frac{di}{dt}\right|=\left|\frac{{\mu }_0{N}_1{N}_2{S}_1}{l_1}\frac{d{i}_1}{dt}\right|$

$=\frac{(4\pi \times {10}^{-7})\left(25\right)\left(10\right)(5\times {10}^{-4})\left(0.2\right)}{{10}^{-2}}=3.14\times {10}^{-6}V$