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A square loop of side 12 cm with its sides parallel to X and velocity of 8 cm s in the positive x-direction in an environment containing a magnetic field in the positive z-direction. The field is neither uniform in space nor constant in time. It has a gradient of 10 T cm along the negative x-direction (that is it increases by 103 T cm- as one moves in the negative x-direction), and it is decreasing in time at the rate of 103 Ts. Determine the direction and magnitude of the induced current in axes is moved with a the loop if its resistance is 4.50 m2. Sol. Given, side of loop a = 12 cm . Area of loop (A) = a = (12) = 144 cm = 144 x 10 m? (. Area of square = (side)) |
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Answer» Solution :The magnetic field in loop varies with position .x. of loop and also with time SIMULTANEOUSLY. The rate of change of FLUX due to variation of .B. with time is `(d phi)/(dt)=A xx (DB)/(dt)` The rate of change of flux due to variation B with position .x. is `(d phi)/(dt)= A xx (dB)/(dt) -A(dB)/(dx) xx (dx)/(dt)=A(dB)/(dx) vartheta` Since both cause decrease in flux, the two effects will add up `:.` The net emf induced `e=(dphi)/(dt)=A(dB)/(dt)+A(dB)/(dx) xx vartheta=A[(dB)/(dt)+vartheta.(dB)/(dx)]` `=144 xx 10^(-4)[10^(-3)+8 xx 10^(-3)]` `=144 xx 9 xx 10^(-7)=129.6 xx 10^(-6)` V |
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