Electric field — UPSC Physics Optional CSE 2026 Paper I

A very long solenoid of radius a, with n turns per unit length, carries a current I_s. Coaxial with the solenoid, at radius b \gg a, is a circular ring of wire with resistance R. When the current in the solenoid is gradually reduced, a current I_r is induced in the ring. Calculate I_r in terms of \frac{dI_s}{dt}. Also, calculate the power dissipated through Joule effect and the electric field \vec{E} near the solenoid.