Question

The magnetic flux linked with a coil is given by an equation ∅ (in webers) = 8t²+3t+5. The induced e.m.f. in the coil at the fourth second will be
(a) 16 units(b) 39 units(c) 67 units(d) 145 units

Answer 1

answer : option (c) 67 units

explanation : magnetic flux linked with the coil is given by, $\phi=8t^2+3t+5$

we know, induced emf is the negative of rate of change of magnetic flux with respect to time.
e.g., $\xi_{in}=-\frac{d\phi}{dt}$

so, first of all, differentiate magnetic flux with with respect to time,

e.g., $\frac{d\phi}{dt}=16t+3$

at t = 4, $\frac{d\phi}{dt}=16\times4+3=67$

so, induced emf = - $\frac{d\phi}{dt}$ at t = 4
= -67 units

hence, magnitude of induced emf in the coil at the fourth second will be 67 units.