The flux linked with a coil at any instant 't' is given by $$\phi=10 t^{2}-50 t+250$$ The induced emf at $t=3\,\mathrm{s}$ is

JEE Main · 2006 · 30 Apr 2006 · Offline · Electromagnetic Induction

The flux linked with a coil at any instant 't' is given by

ϕ = 10 t^{2} - 50 t + 250

The induced emf at

t = 3 s

(A)190 V
(B)-190 V
(C)-10 V✓ Correct
(D)10 V

Answer: (C)

Solution

The induced emf is minus the rate of change of flux,

ε = - \frac{d ϕ}{d t}

. Differentiating

ϕ = 10 t^{2} - 50 t + 250

gives

\frac{d ϕ}{d t} = 20 t - 50

, so

ε = - (20 t - 50)

. At

t = 3 s

this is

- (60 - 50) = - 10 V

JEE Main · 2006 · 30 Apr 2006 · Offline · Single correct option

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