A charge q is placed at the centre of the line joining two equal po...

Question

A charge q is placed at the centre of the line joining two equal point charges each equal to +Q. The system of three charges will be in equilibrium, if q is equal to:

Accepted Answer

Setup: Let the distance between the two +Q charges be 2a. The charge q is placed at the midpoint, so distance from each +Q to q = a.

Condition for equilibrium of +Q:
Force from other +Q (repulsive) must be balanced by force from q (must be attractive).

Step 1: Force between two +Q charges:
F₁ = kQ²/(2a)² = kQ²/4a²

Step 2: Force on +Q due to q:
F₂ = kQ|q|/a²

Step 3: Balance forces:
kQ²/4a² = kQ|q|/a²
|q| = Q/4

Step 4: For attraction, q must be negative:
q = -Q/4

Answer: Option (D) -Q/4

🔔 Email Updates Lein