A short conductor AB is held parallel to a long thin conductor CD. They carry currents in the same direction. AB is moved (by an external agent) with a constant velocity v, away from CD, in the plane containing AB and CD. AB remains parallel to CD during the motion. The power (P) delivered by the external agent depend on time t as $P\propto t^{-n}$. Find value of n.

Points to remember- where ${\mu }_o$ refers to the permeability of free space

I = magnitude of the electric current in amperes (A)

x = distance in meters (m)

The distance between the conduction,

$x=vt$

Here, magnetic field due to CD on AB = $\frac{{\mu }_{o}I}{2\pi x}$

Also, the force on AB due to a current-carrying conductor CD, F$=\text{BiL}$

and power, P = Fv = BILv =$\frac{{\mu }_{o}I}{4\pi x}\times iLv$

$=\frac{{\mu }_{o}IiL}{4\pi }\times \frac{v}{x}$

$=\frac{{\mu }_{o}IiL}{4\pi }\times \frac{1}{t}$

$\Rightarrow P\propto \frac{1}{t}$