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Four point charge q, - q, 2Q and Q are p...

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.

A

1

B

`(5)/(sqrt(2))`

C

`(2sqrt(2))/(5)`

D

`(5sqrt(5))/(2)`

Text Solution

Verified by Experts

The correct Answer is:
D

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`
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