Three identical charges are placed on three vertices of a square. If the force acting between `q_(1)` and `q_2` is `F_(12)` and between `q_(1)` and `q_(3)` is `F_(13)`, then = ..........

Options

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

Answer

C

Explanation

Suppose the length of square is .a. and hence length of diagonal is `sqrt(2a)`

`F_(12) = (k(q)(q))/a^(2) = (kq^(2))/a^(2)` and `F_(13) = (k(q)(q))/(sqrt(2)a)^(2) = (kq^(2))/(2a^(2))`
`therefore F_(13)/F_(12) = 1/2`