Question

The magnetic flans associated with a metal ring varies with time all. to $\varphi =3(a{t}^3-b{t}^2)$ $T{m}^2,a=2se{c}^{-3},b=6se{c}^{-2}$. If the resistance of the ring is $24\Omega$, the current induced in the ring during the time $t=2$ sec is

• A. $2amp$
• B. $4amp$
• C. $6amp$
• D. $zero$

Answer 1

The correct option is D $zero$

Given,

$\varphi =3(a{t}^3-b{t}^2)T{m}^2$

$a=2se{c}^{-3}$

$b=6se{c}^{-3}$

$R=24\Omega$

The induced emf

$e=IR=\frac{d\varphi }{dt}=3(3a{t}^2-2bt)$

$I=\frac{3}{R}(3a{t}^2-2bt)$

At $t=2sec$

$I=\frac{3}{24}(3\times 2\times 4-2\times 6\times 2)$

$I=0$ $amp$

The correct option is D.