A cavotu pf radous `r` is present inside a solid dielectric sphere of radus ` R`, having a volume charge density of ` rho`. The distance bhetween the centres of the sphere and the cavity is a . An electron `e` is kept inside the cavity at an angle ` theta = 45^@` as shown . how long will it take to touch the sphere again ?
` .

Answer

` sqrt (( 6 sqrt 2m r varepsilon_0)/(erhoa))`

Explanation

Let us assume that the empty is filled with charge of charge denstiy (+ prop )& ( - prop) If we consider ` + prop` charge density then elctric field at `P`,
`vec E_(p) = vec E_(+ prop) + vec E_(-prop) = (prop)/(3 in_0) [ vec (OP) + vec (PO)] = (prop)/(3 in_0) overline (OO)`
` vec E_P = (prop)/(3 in_0) overlinea`
Let electron will strike at (P)`
` Pp' = 2 r cos 45^@ = R/(sqrt 2)

From equation of motion
`sqrt 2 r = 1/2 xx at^2 rArr sqrt 2 = 1/2 xx (eE)/m t^2` ...(2)
From (1) and (2)
`sqrt 2 r = 1/2 e/m (propa)/(3 in_0) t^2 rArr = sqrt ((6 sqrt 2 m in_0r)/(epropa))`.