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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 8cms^(-1) in the possitive 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)Tcm^(-1) along the negative x-direction (that is it increases by 10^(-3)T as one moves in the negative x-direction), and it is decreasing in time at the rate of 10^(-3)Ts^(-1). Determine the direction and magnitude of the induced current in the loop of its resistance is 4.50mOmega. |
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Answer» Solution :RATE of change of FLUX due to time variation in `B=144xx10^(-4)m^(2)xx10^(-3)TS^(-1)` `=1.44xx10^(-5)Wb//s` Rate of change of flux due to motion of the loop in nonuniform `B=144xx10^(-4)m^(2)xx10^(-3)Tcm^(-1)xx8cm//s=11.52xx10^(-5)Wb//s` Net change in flux = `varepsilon=(1.44+11.52)xx10^(-5)=12.96xx10^(-5)V` Current `I=(12.96xx10^(-5))/(4.5xx10^(-3))=2.88xx10^(-2)A` Direction of induced current is such that it INCREASES the magnetic flux LINKED with the loop in the positive direction. |
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