Discussion Forum



1)

The current density varies with radial distance r as J = ar2, in the cylindrical wire of radius R.The current passing through the wire between radial distance R/3 and R/2 is 


A) $\frac{65\pi a R^{4}}{2592}$

B) $\frac{25\pi a R^{4}}{72}$

C) $\frac{65 \pi a^{2} R^{3}}{2938}$

D) $\frac{81 \pi a^{2} R^{4}}{144}$

Answer:

Option A

Explanation:

Given , J= a r2

$i= \int_{1}^{2}  J\times 2\pi r dr=\int_{R/3}^{R/2}  ar^{2}\times 2\pi r dr$

    =$2\pi a\int_{R/3}^{R/2}  r^{3} dr = 2 \pi a |\frac{r^{4}}{4}|_{R/3}^{R/2}$

$=\frac{\pi a}{2}\left[ (\frac{R}{2})^{4}-(\frac{R}{3})^{4}\right]$

  $=\frac{\pi a R^{4}}{2}\times\frac{65}{81\times 16}$= $\frac{65\pi a R^{4}}{2592}$