Question

A 3.0-cmcm-diameter, 12-turn coil of wire, located at zz = 0 in the xyxy-plane, carries a current of 7.5 AA. A 2.0-mmmm-diameter conducting loop with 2.02.0 ×× 10−4−4 ΩΩ resistance is also in the xyxy-plane at the center of the coil. At tt = 0 ss, the loop begins to move along the zz-axis with a constant speed of 75 m/sm/s.

Part A What is the induced current in the conducting loop at tt = 200 μsμs? The diameter of the conducting loop is much smaller than that of the coil, so you can assume that the magnetic field through the loop is everywhere the on-axis field of the coil.

Answer 1

Diameter =3cm , N = 12 twins coil current, I = T.SA loop diameter = 2mm , R= 2x104 75 mis speed = to zoofs , Tend = 2 Magnetic field on the axis of coil R242) 3/2 dot IATI Pz (flux) = to 2N I TRY THE faraday's law, End = |dte) = o XQNI X + R2 23 xazu (R²4 22h At t= 200 ks, 2=ut = 75*200 x16= 0.015 Eind = 107 x 2x 12x7.5 X ² x 0. 015² x 0.001243 X 2x0.015 x 75 @.0is² +0.0152) 512 Eind = 3.14 Xios volt Linde = Eind 3.14x10s 2x104 R Oo157 A

0.157 A