Ask Questions, Get Answers

Want to ask us a question? Click here
Browse Questions
0 votes

The point $\;r_{m}\;$ inside the sphere of a sphere of radius R at which electric field intensity is maximum , is given by


Can you answer this question?

1 Answer

0 votes
Answer : $\;r_{m}=\large\frac{2R}{3}$
Explanation :
Outside the ball electric field = $\;\large\frac{\rho_{0} R^3}{12 R^2 \in_{0}}$
It will be maximum when $r=R$
Then ,
$E_{r}=\large\frac{\rho R^3}{12 R^2 \in_{0}}=\large\frac{\rho_{0} R}{12 \in_{0}}$
Inside the ball $\;E_{r}=\large\frac{\rho_{0}}{\in_{0}}\;[\large\frac{r}{3}-\large\frac{r^2}{4R}]$
For $\;E_{r}\;$ to be max
$\large\frac{d E_{r}}{dr}=0$
$\large\frac{d^2 E_{r}}{dr^2}=-\large\frac{\rho_{0}}{2 \in_{0} R} < 0$
Hence at $\;r=\large\frac{2R}{3}\;E_{r}\;$ is maximum and is greater than at $\;r=R\;.$
answered Feb 18, 2014 by yamini.v
edited Mar 13, 2014 by balaji.thirumalai

Related questions

Ask Question
student study plans
JEE MAIN, CBSE, AIPMT Mobile and Tablet App
The ultimate mobile app to help you crack your examinations
Get the Android App