Question

Two identical non-conducting spherical shells having equal charge Q, which is uniformly distributed on it, are placed at a distance d apart, from where they are released. Find out kinetic energy of each sphere when they are at a large distance.

Answer 1

Formula,

$F=\frac{1}{4\pi {\epsilon }_0}\frac{Q^2}{d^2}$

$KE={\int }_d^{r}Fdr={\int }_d^r\frac{1}{4\pi {\epsilon }_0}\frac{Q^2}{d^2}dr=\frac{Q^2}{4\pi {\epsilon }_0}{[-\frac{1}{r}]}_d^r$

$\therefore KE=\frac{Q^2}{4\pi {\epsilon }_0}[\frac{1}{d}-\frac{1}{r}]$

where, r is the maximum distance of identical spherical charges from each other