In the given figure, two point chrges `q_(1) " and " q_(2)` are placed at distances a and b from centre of a metallic sphere having charge Q.Find electric felds due to the metallic sphere at the point P.

Options

A. `(1)/(4pi epsilon_(0)) sqrt(((q_(1))/(a))^(2)+((q_(2))/(b^(2)))^(2))`
B. `(1)/(4pi epsilon_(0))(Q)/(R^(2))`
C. `(1)/(4pi epsilon_(0)) sqrt(((Q)/(R^(2)))^(2)+((q_(1))/(a^(2))+(q_(2))/(b^(2)))^(2))`
D. None of the above

Answer

A

Explanation

The net electric field at P is zero.
`vec(E)_(P) = vec(E)_(1)+vec(E)_(2) +vec(E)_("sphere")`
`0 = vec(E)_(1) +vec(E)_(2)+ vec(E)_("sphere")`
`:. vec(E)_("sphere") =- (vec(E)_(1)+vec(E)_(2))`
`|vec(E)_("sphere")| = sqrt(E_(1)^(2)+E_(2)^(2))`
`= sqrt(((q_(1))/(4piepsilon_(0)a^(2)))^(2)+((q_(2))/(4piepsilon_(0)b^(2)))^(2))`
`= (1)/(4pi epsilon_(0)) sqrt(((q_(1))/(a^(2)))^(2)+((q_(2))/(b^(2)))^(2))`