Question 166: Electromagnetic Induction

Question

In a coil of resistance $$8 \,\Omega$$, the magnetic flux due to an external magnetic field varies with time as $$\phi=\frac{2}{3}\left(9-t^{2}\right)$$. The value of total heat produced in the coil, till the flux becomes zero, will be _____________ $$J$$.

Accepted Answer

$$R = 8\,\Omega $$
$$\phi  = {2 \over 3}(9 - {t^2})$$
At $$t = 3$$, $$\phi  = 0$$
$$\varepsilon  = \left| { - {{d\phi } \over {dt}}} ight| = {4 \over 3}t$$
$$H = \int_0^3 {{{{V^2}} \over R}dt = \int_0^3 {{1 \over 8} 	imes {{16} \over 9}{t^2}dt} } $$
$$ = {2 \over 9} 	imes \left( {{{{t^3}} \over 3}} ight)_0^3 = {2 \over {9 	imes 3}} 	imes 27 = 2\,J$$

Electromagnetic Induction

In a coil of resistance $8 \,\Omega, the magnetic flux due to an external magnetic field varies with time as \phi=\frac{2}{3}\left(9-t^{2}\right). The value of total heat produced in the coil, till the flux becomes zero, will be _____________ J$.

Integer / Numeric Answer Type