find the magnitude of the electric field at the point P in the configuration shown in figure for `dgtgta, Take2qa = p.`

Options

A. `1/(4piepsilon_0)q/d^2 ` , `1/(4piepsilon_0).p/d^3 ` `1/(4piepsilon_0).(root_((qd)^(2) + p^(2))/d^2`
B. `1/(4piepsilon_0)q/d^2 ` , `1/(4piepsilon_0).p/d^3 ` `1/(4piepsilon_0).(root_((qd) + p^(2))/d^3`
C. `1/(4piepsilon_0)q/d^2 ` , `1/(4piepsilon_0).p/d^2 ` `1/(4piepsilon_0).(root_((qd)^(2) + p^(2))/d^3`
D. `1/(4piepsilon_0)q/d^2 ` , `1/(4piepsilon_0).p/d^3 ` `1/(4piepsilon_0).(root_((qd)^(2) + p^(2))/d^3`

Answer

D

Explanation

`(a) Taking `
` P=2qa,E=1/(4piepsilon_0)q/d^2 `
` E_1sin theta=E_2sin theta `
` So, E=E_1cos theta+E_2 cos theta `
` =E_1cos theta+E_2 cos theta `
` 2E_1cos theta `
` =2(1)/(4piepsilon_0).(qa)/(d^2+a^2)^(3/2) `
` 1/(4piepsilon_0).p/d^3 (:. altltd)`