Faraday’s law — UPSC Physics Optional IFoS 2017 Paper I

(i) State Faraday's law of electromagnetic induction and prove that it can be expressed in the following vector form : \mathrm{Curl}~\vec{E} = -\frac{\partial \vec{B}}{\partial t} with \vec{E} and \vec{B} being the electric and magnetic fields. (ii) A coil of 10 turns has dimension 9~\text{cm} \times 7~\text{cm}. It rotates at the rate of 15\pi~\text{rad/sec} in a uniform field whose flux density is 0\cdot 6~\text{weber/m}^2. What is the maximum e.m.f. induced in the coil ?