Question

A square wire frame shown in the figure is on the x=0 plane at t=0. Then it starts to move with a velocity of v = v_o.$\underset{u}{\rightarrow}$_y. The magnetic flux density is measured as B = B_o = siny.cos2t.$\underset{u}{\rightarrow}$_x + sinz.sin2t.$\underset{u}{\rightarrow}$_y. Find the voltage induced on the frame.

(The edge length of square frame is a.)

Answer 1

Vertical-bar e Vertical-bar = d phi/dt = d/dt(B, A) = AdB/dt = B_0a^2d/dt[sin y cos 2tu_x^rightarrow + sinz sin 2t u_y^rightarrow] = B_0a^2[cos 2t cosy dy/dt + siny(- sin 2t).2 + sin 2t cos Z dz/dt + sinz cos 2t . 2] v = v_0u_y^rightarrow dy/dt = v_0 dz/dt = v_0 dz/dt = 0 = B_0a^2[cos 2t cosy v_0 - 2 siny sin 2t + 2 sinz cos 2t] = B_0a^2[cos 2t(v_0 cosy + 2 sinz) - 2 sin y si9n 2t]