Define mutual inductance and write its $\mathrm{S}.\mathrm{I}.$ unit.

A conducting rod PQ of length $20 \mathrm{cm}$ and resistance $0.1 \Omega$ rests on two smooth parallel rails AA' and CC' of negligible resistance. It can slide on the rails and the arrangement is positioned between poles of a permanent magnet producing uniform magnetic field $B=0.4 \mathrm{T}$. The rails, the rod and the magnetic field are in three mutually perpendicular directions as shown in the figure. If the ends A and C of the rails are short-circuited, find the external force required to move the rod with uniform velocity $v=10 \mathrm{m}/\mathrm{s}$.

A conducting rod PQ of length $20 \mathrm{cm}$ and resistance $0.1 \Omega$ rests on two smooth parallel rails AA' and CC' of negligible resistance. It can slide on the rails and the arrangement is positioned between poles of a permanent magnet producing uniform magnetic field $B=0.4 \mathrm{T}$. The rails, the rod and the magnetic field are in three mutually perpendicular directions as shown in the figure. If the ends A and C of the rails are short-circuited, find the power required to move the rod with uniform velocity $v=10 \mathrm{m}/\mathrm{s}$.