1. The problem statement, all variables and given/known data A ring of radius R is kept in the xy plane and a constant uniform magnetic field exists of magnitude B in the -k direction (negative z direction ) . It is heated through a temperature T . If the resistance of the ring is R1find the final radius of the ring. Coefficient of linear expansion : α , mass of ring is m. Note: this is not a question I picked up from a textbook, but I am confused about the outcome. I ask this question out of curiousity. 2. Relevant equations E = -dφ/dt r = R(1+αΔT) whereΔT is change in temperature. dF = idl×B where dl here would be the differential length element that is heated. 3. The attempt at a solution I calculated the magnitude of induced emf , as function of r, E= B 2πr dr/dt, I put dr/dt = α dT/dt, where T is absolute temperature As this question is a conceptual doubt I assumed the absolute temperature T to be a function of t (a linear polynomial, T = at2+ bt +c So I got the current in the ring as I = 2πR2 B α (2at+b)/R1 I knew that when we pull a straight rod through a magnetic field in a direction perpendicular to the magnetic field a mechanical force acts against the force of our hand equal to ilB where i = Blv/R where r is the resistance of the rod , the mass of the rod given to be m , it attains a terminal velocity which can be calculated by putting, a = ilB/m = dv/dt So I thought that a retarding force would contract the ring, and when I checked ilB for the ring was radially inwards. Which made me think about the terminal velocity or terminal radius of the ring. The confusion: I could calculate the retarding acceleration of only the differential element dl , but how do I relate it to the whole ring . Also finally what equation of motion do i write for this element. Please tell me if I am thinking in the right direction or if I should stop thinking about this problem if my approach is completely wrong.