john asked in Science & MathematicsPhysics · 6 years ago

# Electrostatic Forces?

Charges Q and q are stationary at opposite corners of a square with side a as shown in the figure. Assume that Q is a positive charge. Derive an expression for the value of charge q in terms of the variables of the question so that there is no net force on charge Q. As part of your answer, clearly indicate whether charge q is positive or negative.

The diagram looks like:

Q q

q Q

Relevance
• 6 years ago

F = kqQ / d²

The distance from Q to Q is a√2, so you need q such that

2 * (√2/2) qQ / a² = QQ / (a√2)²

(The LHS comes from the fact that the projection of each side force along the diagonal is cos45º = √2 / 2, and we've got two of them.)

Q and a² cancel;

√2 * q = Q/2

q = Q / 2√2 = Q√2 / 4 ≈ 0.35Q

Of course, q must have negative charge in order to overcome the repulsion between Q and Q,