Question

Figure shows the cross-sectional view of the hollow cylindrical conductor with inner radius 'R' and outer radius '2R', cylinder 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. $\frac{5{\mu }_{0}i}{36\pi R}$

Answer 1

The correct option is D $\frac{5{\mu }_{0}i}{36\pi R}$

By using $B=\frac{{\mu }_{0}i}{2\pi r}\left(\frac{r^2-a^2}{b^2-a^2}\right)$ here $r=\frac{3R}{2},a=R,b=2R$
$\Rightarrow B=\frac{{\mu }_{0}i}{2\pi \left(\frac{3R}{2}\right)}\times \left\{\frac{{\left(\frac{3R}{2}\right)}^2-R^2}{\left(2R^2\right)-R^2}\right\}=\frac{5.{\mu }_{0}i}{36\pi R}$.