Discussion

The flux linked with a coil at any instant is given by \(\phi = 5t^{2} - 25t - 150\) (in SI unit). The emf induced in the coil at \(t = 2s\) is

Answer: A

The induced emf is +5 V.

By Faraday's law, \(\varepsilon = -\frac{d\phi}{dt}\):

\[ \begin{aligned} \frac{d\phi}{dt} &= 10t - 25 = 20 - 25 = -5 \\ \varepsilon &= -(-5) = +5\ \text{V} \end{aligned} \]

-5 V forgets the minus sign of Lenz's law, and the constant term 150 plays no part, since it does not change with time.

The positive sign means the induced emf opposes the decrease in flux that is happening at that instant (the flux is decreasing at 5 Wb s^-1).

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