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Figure shows a uniformly charged thin no...

Figure shows a uniformly charged thin non-conducting sphere of total charge Q and radius R. If point charge q is situated at point 'A' which is at a distance `r lt R` from centre of the sphere, then find out following :
(i) Force acting on charge q.
(ii) Electric field at centre of sphere.
(iii) Electric field at point B.

Text Solution

Verified by Experts

(i) Electric field inside a hollow sphere = 0
`:.` Force on charge q.
`F = qE = q xx 0 = 0`
(ii) Net electric field at centre of sphere
`E_("net") = vec(E)_(1) + vec(E)_(2)`
`E_(1)` = field due to sphere = 0

`E_(2)` = field due to this charge `= (Kq)/(r^(2))`
(iii) Electric field at B due to charge on sphere, `vec(E)_(1) = (KQ)/(r_(1)^(2))hat(r )_(1)` and due to charge on sphere, `vec(E)_(2) = (Kq)/(r_(2)^(2))hat(r )_(2)`
So, `vec(E)_("net") = vec(E)_(1) + vec(E)_(2) = (KQ)/(r_(1)^(2))hat(r )_(1) + (Kq)/(r_(2)^(2))hat(r )_(2)`
where `r_(1) = CB` and `r_(2) = AB`
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