For a solenoid derive the magnetic energy stored in it, in terms of magnetic field, area of cross-section and it's length.

A coil $Q$ is connected to low voltage bulb $B$ and placed near another coil $P$ as shown in Fig. 6.74. Give reasons to explain the following observation:

The bulb '$B$' lights.

What is the magnetic energy stored in the solenoid? How does this magnetic energy compare with the electrostatic energy stored in a capacitor?

A $50 \mathrm{mH}$ coil carries a current of $2 \mathrm{A}$, the energy stored in joule is

A conducting wire $\mathrm{XY}$ of mass $m$ and neglibile resistance slides smoothly on two parallel conducting wires as shown in Figure. The closed circuit has a resistance $R$ due to $\mathrm{AC}, \mathrm{AB}$ and $\mathrm{CD}$ are perfect conductors. There is a magnetic field $\mathrm{B}=\mathrm{B}\left(\mathrm{t}\right)\hat{\mathrm{k}}$.

For (b), show that the decrease in kinetic energy of $\mathrm{XY}$ equals the heat lost in $R$.