Question

Two coils (#1 and #2) made out of the same wire are in a uniform magnetic field with the coil axis aligned in the field direction. Coil #1 has 10 turns of loop with a radius of 5 cm and coil #2 has 5 turns with a radius of 10 cm. Now the field strength is doubled in 2 s. What is the ratio of the emf induced in each coil (emf1 : emf2). The answer is 1:2 but HOW?

Answer 1

flux linkage through and y cloned loop of Area A in a magnetic field B which in axial direction of the loop in given by & = BA for circular loop A = piR^2 R = radius of the loop now if the loop has N turns then the flux linkage is NBA now induced emf elementof = dphi/dt = > elementof =dNBA/dt = NA dB/dt [A A is fixed] Fon first loop elementof_1 = 10 times pi times R^2 times dB/dt [N=10] R =5cm =10 times pi times (5)^2 dB/dt fon second loop elementof_2 = 5 times pi times (10)^2 dB/dt [N =5 R =10cm] so elementof_1: elementof_2 = 10 times pi times(5)^2 dB/dt: 5 times pi (10)^2 dB/dt = 1: 2 here dB/dt in same for the both loop an same amount of magnetic field in changed in same time for both of the loop