A uniform magnetic field of \( 0.1\,\mathrm{Wb\,m^{-2}} \) extends over a plane circuit of area \( 1\,\mathrm{m^{2}} \) and is normal to it. How quickly must the field be reduced to zero if an emf of 100 V is to be produced?
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → \( 10^{-3}\,\mathrm{s} \)
By Faraday’s law, the magnitude of the induced emf is the rate of change of magnetic flux. The field is normal to the circuit, so the flux \( BA \) falls to zero in the time \( \Delta t \), and \( \varepsilon=BA/\Delta t \).
The initial flux is:
\( \begin{aligned} \Phi &= BA \\ &= 0.1\,\mathrm{Wb\,m^{-2}}\times1\,\mathrm{m^{2}} \\ &= 0.1\,\mathrm{Wb} \end{aligned} \)
The time needed for an emf of 100 V is:
\( \begin{aligned} \Delta t &= \frac{\Phi}{\varepsilon} \\ &= \frac{0.1\,\mathrm{Wb}}{100\,\mathrm{V}} \\ &= 10^{-3}\,\mathrm{s} \end{aligned} \)