Question

A magnetic field of flux density $10T$ acts normal to a coil of $50$ turns having $100$ $c{m}^2$ area. The e.m.f. induced if the coil is removed from the magnetic field in $0.1$ seconds is:

• A. $50V$
• B. $60V$
• C. $80V$
• D. $40V$

Answer 1

The correct option is A $50V$

In this case, $B=10T,N=50turns,A=100c{m}^2={10}^{-2}{m}^2$ and $dt=0.1s$

We know that,

${\varphi }_1=NBACos\theta =NBA$ (as $Cos\theta =Cos0=1$)

Therefore,

${\varphi }_1=50\times 10\times {10}^{-2}=5weber$

When the coil is removed from the magnetic field, $B=0$

So,

${\varphi }_2=0$

Therefore,

${\varphi }_1-{\varphi }_2=d\varphi =0-5=-5weber$.

We also know that $e=-\frac{d\varphi }{dt}=\frac{-5}{0.1}=50V$

Hence, the induced emf if the coil is removed from the magnetic field in $0.1$ second is $50V$.