Figure shows the cross-sectional view of the hollow cylindrical conductor with inner radius $R$ and outer radius $2 R$, carrying uniformly distributed current $i$ along its axis. The magnetic induction at point $P$ at a distance $3 R / 2$ from the axis of the cylinder will be

Question

Aicharya · Accepted Answer

The given situation is shown in the following figure,

We know that, magnetic field induction at point $P$ is given as $ \begin{aligned} B & =\frac{\mu_0}{4 \pi} \cdot \frac{2 i}{O P}\left[\frac{O P^2-R^2}{(2 R)^2-R^2}\right] \\ & =\frac{\mu_0}{4 \pi} \cdot \frac{2 i}{3 R}\left[\frac{\left(\frac{3 R}{2}\right)^2-R^2}{4 R^2-R^2}\right] \\ & =\frac{\mu_0 i}{3 \pi R}\left[\frac{\left(\frac{9 R^2}{4}\right)-R^2}{3 R^2}\right]=\frac{\mu_0 i}{3 \pi R}\left[\frac{5 R^2}{12 R^2}\right] \\ & =\frac{\mu_0 i}{3 \pi R} \times \frac{5}{12}=\frac{5 \mu_0 i}{36 \pi R} \end{aligned} $

Figure shows the cross-sectional view of the hollow cylindrical conductor with inner radius $R$ and outer…

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