Faraday’s law — UPSC Physics Optional CSE 2008 Paper I

State Faraday's Law of induction in terms of emf and magnetic flux. Use Stoke's theorem to express the law in differential form. A uniform, time varying magnetic field \bar{B} = \bar{B}_0(1 + \alpha t)\hat{k} fills a circular region of radius R lying in the x-y plane with the centre at origin. Here \bar{B}_0 and \alpha are appropriately dimensioned constants. Find the induced electric field at a distance r from the centre where r < R.