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A cavity pf radius r is present inside a...

A cavity pf radius `r` is present inside a 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 `e` is kept inside the cavity at an angle ` theta = 45^@` as shown . how long will it take to touch the sphere again ?
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Text Solution

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The correct Answer is:
`sqrt((6sqrt(2)mr in_(0))/(e rho a))`
The direction of electric field inside the cavity in -ve x direction and of constant magnitude `(rho a)/(3 in_(0))`

For touch the sphere again, electron must move `2r cos 45^(@)` (as shown) distance
`:. 1/2 [(rho a)/(3 in_(0))xxe/m]xxt^(2)=sqrt(2)r :. t=sqrt((6sqrt(2)mr in_(0))/(e rho a))`
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