A conducting metal circular-wire-loop of radius r is placed perpendicular to a magnetic field which varies with time as
B = B₀e$${^{{{ - t} \over r}}}$$ , where B₀ and $$\tau $$ are constants, at time t = 0. If the resistance of the loop is R then the heat generated in the loop after a long time (t $$ \to $$ $$\infty $$) is :

Two coaxial solenoids of different radius carry current $$I$$ in the same direction. $$\overrightarrow {{F_1}} $$ be the magnetic force on the inner solenoid due to the outer one and $$\overrightarrow {{F_2}} $$ be the magnetic force on the outer solenoid due to the inner one. Then :

A circular loop of radius $$0.3$$ $$cm$$ lies center of the small loop is on the axis of the bigger loop. The distance between their centers is $$15$$ $$cm.$$ If a current of $$2.0$$ $$A$$ flows through the smaller loop, than the flux linked with bigger loop is

A metallic rod of length $$'\ell '$$ is tied to a string of length $$2$$$$\ell $$ and made to rotate with angular speed $$w$$ on a horizontal table with one end of the string fixed. If there is a vertical magnetic field $$'B'$$ in the region, the $$e.m.f$$ induced across the ends of the rod is