Question

Four equal charges q are placed at the four comers A, B, C, D of a square of length a. The magnitude of the force on the charge at B will be ______.

Options

• `(3"q"^2)/(4piepsilon_0"a"^2)`

• `(4"q"^2)/(4piepsilon_0"a"^2)`

• `((1 + 2sqrt2)"q"^2)/(2 xx 4piepsilon_0 "a"^2)`

• `(((2 + 1)/sqrt2)"q"^2)/(4piepsilon_0"a"^2)`

Answer 1

Four equal charges q are placed at the four comers A, B, C, D of a square of length a. The magnitude of the force on the charge at B will be `underline(((1 + 2sqrt2)"q"^2)/(2 xx 4piepsilon_0 "a"^2))`.

Explanation:

`"F"_"AC" + "F"_"D" = sqrt("F"_"A"^2 + "F"_"C"^2)` since

`"F"_"A" = "F"_"C" = "kq"^2/"a"^2` and

`"F"_"D" = (sqrt2 "kq"^2)/"a"^2 + "kq"^2/(2"a"^2)`

= `"kq"^2/("a"^2)(sqrt2 + 1/2)`

`= "q"^2/(4piepsilon_0"a"^2) ((1 + 2sqrt2)/2)`