Question

The radius of a circular coil having $50$ turns is $2cm$. Its plane is normal to the magnetic field. The magnetic field changes from $2T$ to $4T$ in $3.14sec$. The induced emf in coil will be

• A. $0.4V$
• B. $0.04V$
• C. $4mV$
• D. $0.12V$

Answer 1

The correct option is B $0.04V$

Given that,

Number of turns $N=50$

Magnetic field $B_1=2T$

Magnetic field $B_2=4T$

Time $t=3.14s$

Radius $r=2cm$

Now, the induced e. m. f in coil

$e=\frac{-N(B_2-B_1)A\cos \theta }{dt}$

$e=\frac{-50(4-2)3.14\times {(2\times {10}^{-2})}^2\cos 0^0}{3.14}$

$e=\frac{-50\times 2\times 3.14\times 4\times {10}^{-4}}{3.14}$

$|e|=0.04V$

Hence, the induced e. m. f is $0.04V$