Question

A circuit area $0.01\, m^{2}$ is kept inside a magnetic field which is normal to its plane. The magnetic field changes from $2$ tesla to $1$ tesla in $1$ millisecond. If the resistance of the circuit is $2 \, \Omega$. The rate of heat evolved is

• A. $5\, J/s$
• B. $50\, J/s$
• C. $0.05\, J/s$
• D. $0.5\, J/s$

Answer 1

Answer: (B)

Induced emf, $e=\frac{-d\phi}{dt}$
$\Rightarrow e=\frac{-\left(\phi_{2}-\phi_{1}\right)}{t}=\frac{\left(0.01-0.02\right)}{1\times10^{-3}}$
$e=0.01\times10^{3}=10$ volt
$V=IR$ or $\frac{10}{2}=I$
$\therefore I=5\,A$
Rate of heat evolved $= I^{2}R=\left(5\right)^{2}\times2$
$=25\times2=50J/ s$