A solenoid has 240 turns, a length of 12 cm , and a radius of 2 cm . If the current in the solenoid

Question

A solenoid has 240 turns, a length of 12 cm , and a radius of 2 cm . If the current in the solenoid changes at a steady rate of $0.8 \mathrm{~A} \mathrm{~s}^{-1}$, the magnitude of the emf induced in it is:

Professor PC Thomas Classes · Answer

Self-Inductance $(L)$ : For a long solenoid, $L=\frac{\mu_0 N^2 A}{l}$. - $N=240$ - $l=12 \mathrm{~cm}=0.12 \mathrm{~m}$ - $A=\pi r^2=\pi 	imes(0.02)^2=4 \pi 	imes 10^{-4} \mathrm{~m}^2$ $$ L=\frac{4 \pi 	imes 10^{-7} 	imes(240)^2 	imes 4 \pi 	imes 10^{-4}}{0.12} \approx 7.6 	imes 10^{-4} \mathrm{H} $$ Induced EMF $(\mathcal{E})$ : The magnitude of induced emf is $\mathcal{E}=L\left|\frac{d i}{d t}ight|$. - $\frac{d i}{d t}=0.8 \mathrm{~A} / \mathrm{s}$ Calculation: $$ \begin{gathered} \mathcal{E}=\left(7.6 	imes 10^{-4}ight) 	imes 0.8 \ \mathcal{E} \approx 6.0 	imes 10^{-4} \mathrm{~V} \end{gathered} $$