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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 of 8 cm. s^(-1) 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^(-3)T.cm^(-1) along the negative x-direction and is decreasing in time at the rate of 10^(-3)T.s^(-1). Determine the direction and magnitude of induced current in the loop if its resistance is 4.50 m Omega. |
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Answer» SOLUTION :Rate of change of B DUE to variation with time `=A.(dB)/(dt)=(12xx10^(-2))^(2)xx10^(-3)` `=1.44xx10^(-5)Wb.s^(-1)` Rate of change of B due to variation with space `=A.(dB)/(dx).(dx)/(dt)=(12xx10^(-2))^(2)xx10^(-3)xx8xx10^(-2)` `=11.52xx10^(-5)Wb.s^(-1)` Total rate of change of flux `=(1.44+11.52)xx10^(-5)Wb.s^(-1)` `=12.96xx10^(-5)Wb.s^(-1)` `THEREFORE e=12.96xx10^(-5)V` `therefore I=(e)/(R)=(12.96xx10^(-5))/(4.5xx10^(-3))=2.88xx10^(-2)A` |
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