A cavity of radius r is present inside a fixed solid dielectric sphere of radius R, having a volume charge density of `rho`. The distance between the centres of the sphere and the cavity is a. An electron is released inside the cavity at an angle `theta = 450` as shown. The electron (of mass m and charge –e) will take `((Psqrt(2)mrepsilon_(0))/(earho))^(1//2)` time to touc the sphere again. Neglect gravity. find the value of P:

Explanation

Electric field inside the cavity `=(rhoveca)/(3epsilon_(0))` [here `veca=` along line joining centres of sphere and cavity]
froce on the electron inside the cavity `=(rhoveca)/(3epsilon_(0))` (e) ltrgt Now for distance `d=sqrt(r^(2)+r^(2))=sqrt(2)r`
by `S=ut+1//2at^(2),sqrt(2)r=(1)/(2)xx(rhoae)/(3mepsilon_(0))t^(2)" "impliest=((6sqrt(2)rmepsilon_(0))/(earho))^(1//2)`