Question

Four charges equal to - Q are placed at the four a corners of a square and charge q is at its centre. If the system is in equilibrium, the value of q is ______.

Options

• `-"Q"/4(1+2sqrt2)`

• `"Q"/2(1+2sqrt2)`

• `-"Q"/2(1+2sqrt2)`

• `"Q"/4(1+2sqrt2)`

Answer 1

Four charges equal to - Q are placed at the four a corners of a square and charge q is at its centre. If the system is in equilibrium, the value of q is `bbunderline("Q"/4(1+2sqrt2))`.

Explanation:

Let the square is of side a.

Force |F₁| = `"KQ"^2/"a"^2` where K = `1/(4piepsilon_0)`

|F₂| = `"KQ"^2/(sqrt2"a")^2`

|F₃| = `"KQq"/(("a"/sqrt2)^2)`

As the system is in equilibrium, thus net force is equal to zero.

`sqrt2"KQ"^2/"a"^2+"KQ"^2/((sqrt2"a")^2)="KQq"/(("a"/sqrt2)^2)`

⇒ q = `"Q"/4(1+2sqrt2)`