It is required to hold equal charges q in equilibrium at the corners of a square. What charge when placed at the center of the square will do this?

Question

It is required to hold equal charges q in equilibrium at the corners of a square. What charge when placed at the center of the square will do this? (A) -(q/2)(1+2 √2) (B) (q/2)(1+2 √2) (C) (q/4)(1+2 √2) (D) -(q/4)(1+2 √2)

Tardigrade Admin · Accepted Answer

A C=√2 l=B D or B O=(1/√2) <img class="img-fluid question-image" alt="image" src="https://cdn.tardigrade.in/img/question/physics/04370076c3872b4bcd7d6c1ae34d5198-.png" /> FB O=FB D+(FB A+FB C) cos 45°. Solving, we get Q=(q/4)(1+2 √2) and Q should be negative of q .

Q. It is required to hold equal charges $q$ in equilibrium at the corners of a square. What charge when placed at the center of the square will do this?

$- \frac{q}{2} (1 + 22)$

$\frac{q}{2} (1 + 22)$

$\frac{q}{4} (1 + 22)$

$- \frac{q}{4} (1 + 22)$

$A C = 2 l = B D$
or $BO = \frac{1}{2}$

$F_{BO} = F_{B D} + (F_{B A} + F_{BC}) cos 4 5^{\circ}$ .
Solving, we get
$Q = \frac{q}{4} (1 + 22)$ and $Q$ should be negative of $q .$

Q. It is required to hold equal charges q in equilibrium at the corners of a square. What charge when placed at the center of the square will do this?

−2q​(1+22​)

2q​(1+22​)

4q​(1+22​)

−4q​(1+22​)