Four point charge `q, - q, 2Q` and Q are placed in order at the corners A, B, C and D of a square. If the field at the midpoint of CD is zero then the value of `q//Q` is `(5 sqrt5)/(x)`. Find the value of x.

Options

A. 1
B. 2
C. `(2sqrt(2))/(5)`
D. `(5sqrt(5))/(2)`

Answer

D

Explanation

`E_(1) = (kq)/((sqrt(5)b)^(2)) = (kq)/(5b^(2))`
`E_(2) = (kQ)/(b^(2)), E_(1) = (2kQ)/(5b^(2))`
`E_("net") = 2E_(1) cos theta +E_(2)-E_(3)`
`0 + (2kq)/(5b^(2)) xx (1)/(sqrt(5)) + (kQ)/(b^(2)) - (2kQ)/(b^(2))`
`(q)/(Q) = (5sqrt(5))/(2)`