Q. A varying magnetic flux linking a coil is given by $\phi - X\ t^{2}.$ If at time t =3 s, the emf induced is 9V, then the value of X is
A) $0.66\ {Wbs}^{- 2}$
B) $1.5\ {Wbs}^{- 2}$
C) $- 0.66\ {Wbs}^{- 2}$
D) $- 1.5\ {Wbs}^{- 2}$
Explanation
(b) From Faraday’s law, induced emf is
$\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ e = - \frac{d\phi}{dt}$
Given , $\phi = Xt^{2}$
$\therefore\ \ \ \ \ \ \ \ \ \ \ \ \ e = \frac{- d(Xt^{2})}{dt} = - 2tX$
Given, $t = 3,\ \ \ \ e = 9V$
$\therefore\ \ \ \ \ \ X = \frac{9}{3 \times 2} = 1.5Wbs^{- 2}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.