Question

A $50$ turn circular coil has a radius of $3$cm, it is kept in a magnetic field acting normal to the area of the coil. The magnetic field B is increased from $0.10T$ to $0.35T$ in $2$ milli second, the average induced emf will be

• A. $177V$
• B. $1.77V$
• C. $0.177V$
• D. $17.7V$

Answer 1

The correct option is B $1.77V$

Average flux in the beginning$=\pi r^{2}n{B}_1$

Average flux in the final $=\pi r^{2}n{B}_2$

Increase in flux $d\varphi =\pi r^{2}n(B_2-B_1)$

$=3.14\times (0.03{)}^2\times 50(0.35-0.10)$

$=3.14\times 45\times 25\times {10}^{-7}$

Given time $dt=2\times {10}^{-3}$

$e=\frac{d\varphi }{dt}=\frac{3.14\times 45\times 25\times {10}^{-7}}{2\times {10}^{-3}}$

$=1.77V$(approx)