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A square loop of side 10 cm and resistan...

A square loop of side 10 cm and resistance `0.5Omega` is placed vertically in the east-west plane. A uniform magnetic field of 0.10 T is set up across the plane in the north-east direction. The magnetic field is decreased to zero in 0.70 s at a steady rate. Determine the magnitudes of induced emf and current during this time-interval.

Text Solution

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The angle `theta` made by the area vector of the loop with the magnetic field is `45^(@)`.
The initial magnetic flux is, `phi=BAcostheta=(0.1xx10^(-2))/(sqrt(2))Wb`
Final flux, `phi_("min")=0`
The change in flux is brought about in 0.70s. The magnitude of the induced emf is given by `epsilon=(|Deltaphi_(B)|)/(Deltat)=(|(phi-0)|)/(Deltat)=(10^(-3))/(sqrt(2)xx0.7)=1.0mV`
And the magnitude of the current is `I=(epsilon)/(R)=(10^(-3)V)/(0.5Omega)=2mA`
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