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 0.02 tesla to 0.01 tesla in 1 millisecond. If the resistance of the circuit is 2$\Omega$. The rate of heat evolved is

• A. 5 J/s
• B. 0.5 J/s
• C. 0.05 J/s
• D. 0.005 J/s

Answer 1

The correct option is D 0.005 J/s

Given:

Circuit Area$A=.01m^2$

Magnetic field $B_i=0.02B_f=0.01$

Induced emf, = $e=\frac{-d\varphi }{dt}$

$\Rightarrow e=\frac{-({\varphi }_2-{\varphi }_t)}{t}=\frac{-(0.01-0.02)\times 0.01}{1\times {10}^{-3}}$

$V=e=0.1volt$

$V=IR$

or $I=\frac{0.1}{2}$

$\therefore I=.05A$

Rate of heat evolved $=I^{2}R=(.05{)}^2\times 2=25\times 2=0.005J/s.$