A circular coil of radius 10 cm has 500 turns. A magnetic field which is directed perpendicular to its plane is increasing at a rate of 0.5 T/s. If the resistance of the coil is 5 Ω. Find the current induced in the coil.
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → 1.57 A
By Faraday's law the emf induced in a coil of N turns is \( \varepsilon = N\frac{d\Phi}{dt} \) in magnitude. The field is perpendicular to the plane of the coil, so \( \Phi = BA \) and \( \frac{d\Phi}{dt} = A\frac{dB}{dt} \). The current then follows from Ohm's law.
\( A = \pi r^{2} = 3.14\times(0.1\,\mathrm{m})^{2} = 0.0314\,\mathrm{m^{2}} \)
\( \varepsilon = NA\frac{dB}{dt} = 500\times0.0314\times0.5\,\mathrm{V} = 7.85\,\mathrm{V} \)
\( \displaystyle I = \frac{\varepsilon}{R} = \frac{7.85\,\mathrm{V}}{5\,\Omega} = 1.57\,\mathrm{A} \)