The magnetic flux through a coil varies with time as \( \Phi_B=(6t-t^{2})\,\mathrm{mWb} \), where t is in seconds. At what instant does the current induced in the coil reverse its direction?
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 3 s
By Faraday’s law, \( \varepsilon=-d\Phi_B/dt \). The induced current changes its direction when the emf changes its sign. This happens at the instant the flux stops increasing and starts decreasing.
The emf at any instant is:
\( \begin{aligned} \varepsilon &= -\frac{d\Phi_B}{dt} \\ &= -(6-2t)\,\mathrm{mV} \end{aligned} \)
The emf becomes zero when:
\( 6-2t=0 \)
\( \Rightarrow\; t=3\,\mathrm{s} \)
Before \( t=3\,\mathrm{s} \) the emf is negative, and after it the emf is positive. So the induced current reverses its direction at \( t=3\,\mathrm{s} \). At this instant the flux reaches its largest value, 9 mWb.