If current density in a conducting wire is proportional to the distance r from the axis of the conductor, then find magnetic field at the position $r < R$ , where R is the radius of cross section of the conductor. ('i' is the current in conducting wire)

see full answer

Talk to JEE/NEET 2025 Toppers - Learn What Actually Works!

Real Strategies. Real People. Real Success Stories - Just 1 call away

An Intiative by Sri Chaitanya

\frac{μ_{0} i r^{2}}{2 π R^{3}}

\frac{μ_{0} i r^{2}}{4 π R^{3}}

\frac{μ_{0} i r^{2}}{2 π R^{2}}

\frac{μ_{0} i r^{2}}{2 π R^{4}}

answer is A.

(Unlock A.I Detailed Solution for FREE)

Ready to Test Your Skills?

Check your Performance Today with our Free Mock Test used by Toppers!

Take Free Test

Detailed Solution

$d I = I . dA$

$d I = Kr (2 π r . dr)$

$d I = K .2 π r^{2} . dr$

$= \int_{O}^{R} K .2 π r^{2} . dr$

$I = \frac{2}{3} K {[r^{3}]}_{O}^{R} = \frac{2}{3} π {KR}^{3}$

$\frac{I_{i n}}{I} = \frac{r^{3}}{R^{3}}$

$∴ B = \frac{μ_{0} I_{i n}}{2 π r} = \frac{μ_{0} I r^{3}}{2 π r {.R}^{3}}$

$B = \frac{μ_{0} I r^{2}}{2 π R^{3}}$

JEE

NEET

Foundation JEE

Foundation NEET

CBSE