A coaxial cable having radius "a" of inner wire and inner and outer radii "b" and "c" respectively of the outer shell carries equal and opposite currents of magnitude i on the inner and outer conductors as shown. What is the magnitude of the magnetic induction at point P of the cable at a distance r (b < r

Engineering

Physics

Magnetic Field

Question

A coaxial cable having radius "a" of inner wire and inner and outer radii "b" and "c" respectively of the outer shell carries equal and opposite currents of magnitude i on the inner and outer conductors as shown. What is the magnitude of the magnetic induction at point P of the cable at a distance r (b < r < c) from the axis?

$\frac{μ_{0} i}{2 πr}$

$\frac{μ_{0} ir}{2 {πa}^{2}}$

Zero

$\frac{μ_{0} i}{2 πr} \frac{c^{2} - r^{2}}{c^{2} - b^{2}}$

LiveFree JEE Main Previous Year Online Papers Live Free JEE Advance Previous Year Online Papers

College PredictorLive

Know your College Admission Chances Based on your Rank/Percentile, Category and Home State.

Get your JEE Main Personalised Report with Top Predicted Colleges in JoSA

By Ampere's law

B(2πr) = μ₀(i – i')

Now, current density in the outer wire is constant

$\frac{i}{π (c^{2} - b^{2})} = \frac{i^{'}}{π (r^{2} - b^{2})}$

$i^{'} = i (\frac{r^{2} - b^{2}}{c^{2} - b^{2}})$

$∴ B = \frac{μ_{0} i}{2 πr} [1 - \frac{r^{2} - b^{2}}{c^{2} - b^{2}}] = \frac{μ_{0} i}{2 πr} (\frac{c^{2} - r^{2}}{c^{2} - b^{2}})$