Question

Two concentric circular coils, $C _{1}$ and $C _{2}$, are placed in the $XY$ plane. $C_{1}$ has $500$ turns, and a radius of $1\, cm$ . $C _{2}$ has $200$ turns and radius of $20\, cm$ . $C _{2}$ carries a time dependent current $I(t)=\left(5 t^{2}-2 t+3\right)$ A where $t$ is in s. The emf induced in $C _{1}$ (in $mV )$, at the instant $t =1 s$ is $\frac{4}{x} .$ The value of $x$ is _____.

Answer 1

$I=5 t^2-2 t+3$
$\frac{d l}{d t}=10 t-2$
$\text { At }(t=1 sec )\left(\frac{d l }{ dt }\right)=8 A / s$
$\phi=\left(\frac{\mu_0 \times 200 \times 1 \times 100}{2 \times 20}\right) \times \frac{\pi \times 500}{100 \times 100}$
$\therefore \quad e=\left|\frac{d \phi}{d t}\right|=\frac{\mu_0 \times 200 \times 100 \times 500 \times \pi}{2 \times 20 \times 100 \times 100}\left(\frac{d l }{d t}\right)$
$\Rightarrow e=\left|\frac{d \phi}{d t}\right|=\left(\frac{8}{10}\right) m \text { volt }=\frac{4}{5} m \text { volt }$
$x=5$