When a coil is placed in a time dependent magnetic field the power dissipated in it is P . The number of turns, area of the coil and radius of the coil wire are N , A and r respectively. For a second coils number of turns, area of the coil and radius of the coil wire are 2N , 2A and 3r respectively. When the first coil is replaced with second coil the power dissipated in it is 2 , P . The value of is _______.

Step-by-step solution

The induced emf in the coil is given by Faraday's law: E = N A dB dt The resistance of the coil is R = l a , where l is the total length of the wire and a is its cross-sectional area. The length of the wire is l = N (2 R_c) , where R_c is the radius of the coil. Since the area of the coil is A = R_c^2 , we have R_c = A . Thus, l = 2N A . The cross-sectional area of the wire is a = r^2 . Therefore, the resistance is: R = 2N A r^2 N A r^2 The power dissipated in the coil is: P = E^2 R (N A)^2 N A r^2 = N A^ 3/2 r^2 F