Chat with tutor

Ask Questions, Get Answers


An air-cored solenoid with length 30cm, area of cross section $25 cm^2$ and number of turns 500, carries a current of 2.5A. The current is suddenly switched off in a brief time of $10^{-3}S.$ How much is the average back emf induced across the ends of the open switch in the circuit ? Ignore the variation in magnetic field near the ends of the solenoid ?

(A) 65 V
(B) 0.65 V
(C) 6.5 V
(D) 650 V

1 Answer

Given :
$l = 30 cm = 30 \times 10^{-2} m$
$A = 2.5 cm^2 = 25 \times 10^{-4} m^2$
$N = 500$
$I_1 = 2.5$
$I_2 = 0$
$dt = 10^{-3} s$
Induced emf $e = \frac{d \phi}{dt} = \frac{d}{dt} (BA)$
Magnetic field induction B at a point inside the long solenoid carrying current $I$ is
$B = \mu_o n I \; \; \; \; \; \; \; (n = \frac{N}{l})$
$e = N A. \frac{dB}{dt} = A . \frac{d}{dt} (\mu_o \frac{N}{l} I). \frac{dI}{dt}$
$e = 500 \times 25 \times 10^{-4} \times 4 \times 3.14 \times 10^{-7} \times \frac{500}{30 \times 10^{-2}} \times \frac{2.5}{10^{-3}}$
$\therefore e = 6.5 V$
Help Clay6 to be free
Clay6 needs your help to survive. We have roughly 7 lakh students visiting us monthly. We want to keep our services free and improve with prompt help and advanced solutions by adding more teachers and infrastructure.

A small donation from you will help us reach that goal faster. Talk to your parents, teachers and school and spread the word about clay6. You can pay online or send a cheque.

Thanks for your support.
Please choose your payment mode to continue
Home Ask Homework Questions
Your payment for is successful.
Clay6 tutors use Telegram* chat app to help students with their questions and doubts.
Do you have the Telegram chat app installed?
Already installed Install now
*Telegram is a chat app like WhatsApp / Facebook Messenger / Skype.