$(a)\;\sigma\;k\;R\qquad(b)\;2\;\sigma\;k\;R\qquad(c)\;4\;\sigma\;k\;R\qquad(d)\;16\;\sigma\;k\;R$

Want to ask us a question? Click here

Browse Questions

Ad |

0 votes

0 votes

Answer : (c) $\;4\;\sigma\;k\;R$

Explanation : $\;dV=\large\frac{k\;d\;q}{r}$

$dq=\sigma\;(2r\theta)\;dr$

$dV=\large\frac{1}{4\;\pi\;\in_{0}}\;\large\frac{\sigma\;2r\;dr\;\theta}{r}=\large\frac{\sigma}{2\;\pi\;\in_{0}}\;\theta\;dr$

$r=2\;R\;cos\;\theta$

$r=2\;R\;cos\;\theta$

$dr=-2\;R\;sin\;\theta\;d \theta$

$dr=-\large\frac{\sigma}{2\;\pi\;\in_{0}}\;2\;R\;\theta\;sin\;\theta\;d \theta$

$V=\int_{\large\frac{\pi}{2}}^{0}\;dV=\large\frac{\sigma\;R}{\pi\;\in_{0}}\;\int_{0}^{\large\frac{\pi}{2}}\;\theta\;sin\;\theta\;d \theta$

$V=\large\frac{\sigma\;R}{\pi\;\in_{0}}=4\;k\;\sigma\;R\;.$

Ask Question

Take Test

x

JEE MAIN, CBSE, NEET Mobile and Tablet App

The ultimate mobile app to help you crack your examinations

...