Question

A square loop of side $10$cm and resistance of $2\Omega$ is moving in the region of uniform magnetic field of $0.1$T with a velocity $2$ m/s through a distance $1$ m completely inside the field. The dissipated heat is?

• A. Zero
• B. ${10}^{-4}$J
• C. $2\times {10}^{-4}$J
• D. $4\times {10}^{-4}$J

Answer 1

The correct option is C $2\times {10}^{-4}$J

The angle $\theta$ made by the area vector of the coil with the magnetic field $45°$.

Initial magnetic flux is $\Phi =BAcos\theta$

FinalFlux$\Phi min=0$

The change in flux is brought about in $0.70s$.

The magnitude of the induced emf is given by $\epsilon =\frac{\left|\Delta {\Phi }_B\right|}{\Delta T}=\frac{|\Delta \Phi -0|}{\Delta T}$

$\epsilon =\frac{{10}^{-3}}{\sqrt{2}\times 0.7}=1.0mV$

$MagnitudeofCurrentI=\frac{\epsilon }{R}$

Therefore,Magnitude of Current $I=\frac{1.0mV}{0.5\Omega }=2.0mA$