Question

The magnetic flux linked with a coil is given by the equation $\varphi =2t^2-8t+16$. what will be the magnitude of flux linked with the coil, when induced emf in the coil is zero?

• A. $2\text{Wb}$
• B. $4\text{Wb}$
• C. $6\text{Wb}$
• D. $8\text{Wb}$

Answer 1

The correct option is D $8\text{Wb}$

Given,

$\varphi =2t^2-8t+16$

$\therefore$ emf induced in the coil is,

$E=\left|\frac{d\varphi }{dt}\right|=\left|\frac{d}{dt}\right(2t^2-8t+16\left)\right|=4t-8$

Induced emf will be zero when,

$4t-8=0$

$t=2\text{sec.}$

$\therefore$ flux at $t=2\text{sec. is}$

$\varphi =2(2{)}^2-8\times 2+16=8\text{Wb}$

Hence, option ($D$) is the correct answer.