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A square loop of side 12 cm with its sides parallel to x and y-axes is moved with a velocity 8 cm/s along positive x-direction in an environment containing magnetic field along +ve z-direction. The field has a gradient of 10^(-3)tesla/em along -ve x-direction (increasing along -ve x-axis) and also decreases with time at the rate of 10^(-3)tesla/s. The emf induced in the loop is |
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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 `(dphi)/(DT) = A xx (dB)/(dt)` The rate of change of flux due to variation B with position .x. is `(dphi)/(dt) = A xx (dB)/(dt) = A (dB)/(dx) xx (dx)/(dt) = A (dB)/(dx) xx v ` Since both cause DECREASE in flux, the two effects will add up ` therefore ` The net emf INDUCED ` e = (dphi)/(dt) = A (dB)/(dt) + A(dB)/(dx) xx v= A [ (dB)/(dt) + v (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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