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. `(5)/(sqrt(2))`
C. `(2sqrt(2))/(5)`
D. `(5sqrt(5))/(2)`

Answer

D

Explanation

Field at P due to q and -q
`2. q/(4 pi e_0 (a^2+a^2//4)) . (a//2)/sqrt(a^2+a^2//4) towards C`
Towards C and field at P due to Q and `2Q= Q/(4 pi e_0 a^2//4) towards D`
If net field is zero `implies (2q)/(5sqrt5 pi e_0 a^2) =Q/( pi e_0 a^2) implies q/Q =(5sqrt5)/2`