Q. Figure shows the cross-sectional view of the hollow cylindrical conductor with inner radius ‘$R$’ and outer radius ‘$2R$’. Cylinder is carrying uniformly distributed current along it’s axis. The magnetic induction at point ‘$P$’ at a distance $\frac{3R}{2}$ from the axis of the cylinder will be
A) Zero
B) $\frac{5\mu_{0}i}{72\pi\ R}$
C) $\frac{7\mu_{0}i}{18\pi\ R}$
D) $\frac{5\mu_{0}i}{36\pi\ R}$
Explanation
(d) By using $B = \frac{\mu_{0}i}{2\pi r}\left( \frac{r^{2} - a^{2}}{b^{2} - a^{2}} \right)$, here $r = \frac{3R}{2},a = R,\ b = 2R,$
We get $B = \frac{\mu_{0}i}{2\pi\left( \frac{3R}{2} \right)} \times \left\{ \frac{\left( \frac{3R}{2} \right)^{2} - R^{2}}{(2R)^{2} - R^{2}} \right\} = \frac{5.\mu_{0}i}{36\pi\ R}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.