Question

A spherical cavity of radius 2m is made whose centre is at a distance of 2 m from centre of a uniformly charged solid sphere of density $\rho =8.85\times {10}^{-12}C/m^3$ and radius 5m. If electric field inside cavity is given by x/y N/C, fill value of (y-x).(y & x are minimum possible integers).

Answer 1

For $r<R$
$E\left(r\right)=\frac{\rho }{3{\epsilon }_0}r$
Electric field inside cavity
$\overrightarrow{E}=\frac{\rho r_1}{3{\epsilon }_0}-\frac{\rho r_2}{3{\epsilon }_0}$
$=\frac{\rho }{3{\epsilon }_0}(\overrightarrow{r_1}-\overrightarrow{r_2})=\frac{\rho }{3{\epsilon }_0}\overrightarrow{a}$
$a$ = distance between two centers
$a=2$
$\overrightarrow{E}=\frac{8.85\times {10}^{-12}\times 2}{3\times 8.85\times {10}^{-12}}=\frac{2}{3}=\frac{x}{y}$
$x=2,y=3$
$y-x=3-2=1$