A metallic square frame of edge a is situated in a vertical plane. A uniform magnetic field B is present in the space, directed perpendicular to the plane of the frame. Two boys pull the opposite corners of the square to deform it into a rhombus. They start pulling the corners at t = 0 and displace them at a uniform speed u . If the total resistance of the frame is R , find the induced current in the frame at the ins

Step-by-step solution

Let 2 be the angle at the pulled corners. The diagonals of the rhombus have lengths 2x and 2y , where x = a and y = a . The distance from the center to each pulled corner is x . Since the corners are pulled at a uniform speed u , we have dx dt = u . Differentiating x = a with respect to time t : dx dt = -a d dt = u d dt = - u a The area of the rhombus is A = 1 2 (2x)(2y) = 2a^2 = a^2 2 . The rate of change of area is: dA dt = a^2 ( 2 ) 2 d dt = 2a^2 2 ( - u a ) = -2au 2 When the angle at the pulled corners decrease