Physics - Magnetism Question with Solution | TestHub

The cross-sectional area of the space to be filled is fixed, whilst that of the wire varies as $d^2$. Thus, $n\propto d^{-2}$. The resistance of one turn is inversely proportional to the cross-sectional area of the wire, i.e. varies as $d^{-2}$ and hence the resistance per unit length of the solenoid is $R\propto n{d}^{-2}\propto d^{-4}$. The flux density $B$ is $\propto nI$ and therefore the required current $I\propto n^{-1}\propto d^2$. The heat dissipated per unit length is $R{I}^2$, which $\propto d^{-4}{\left(d^2\right)}^2$, i.e. independent of $d$. Thus, within limits, it does not matter what diameter wire is chosen so far as the heating effect is concerned.