Question

A point charge $Q$ is placed at the centre of the line joining two equal point charges $+q$ and $+q$. The value of $Q$ if the system of the charges is in equilibrium, is

• A. $-\frac{q}{2}$
• B. $-\frac{q}{4}$
• C. $+\frac{q}{4}$
• D. $+\frac{q}{2}$

Hint:

You can determine the sign of $Q$ using basic logic! Since the two outer charges are both positive ($+q$), they naturally repel each other outward. To keep them from flying apart, the central charge $Q$ must be negative to exert an attractive inward force. This immediately eliminates options (C) and (D)!

Answer 1

The Correct Option is B

Step 1: Understanding the Question:
Three collinear charges are in equilibrium. Deduce the sign of the central charge using basic electrostatic logic.

Step 2: Key Formula or Approach:
Like charges repel, opposite charges attract. For static equilibrium, the net force on every charge must be zero. The central charge must counteract the mutual repulsion of the outer charges.

Step 3: Detailed Explanation:
Both outer charges are positive (+q) and naturally repel each other outward. To prevent them from flying apart, the middle charge Q must exert an attractive inward pull on each. This requires Q to be negative. Options suggesting a positive or neutral central charge are physically impossible under these force conditions and can be eliminated immediately.

Step 4: Final Answer:
The central charge Q must be negative, ruling out positive and neutral options.