Question

A known positive charge is located at point P as shown above, between two unknown charges, Q1 and Q2. P is closer to Q2 than Q1. If the net electric force acting on the charge at P is zero, it may correctly be concluded that:

• A. Both Q1 and Q2 are positive
• B. Both Q1 and Q2 are negative
• C. Q1 and Q2 have opposite signs
• D. Q1 and Q2 have the same sign, but magnitude of Q1 is greater than the magnitude of Q2
• E.

Hint:

For the forces to balance out, the charges must have the same sign, and the closer charge must exert a weaker force. This results in a balance of forces.

Answer 1

The Correct Option is D

Let the known positive charge at point $P$ be $+q$.  

We are told that:

• The net electric force on $+q$ is zero
• $P$ is closer to $Q_2$ than to $Q_1$

For the forces to cancel each other:

• $Q_1$ must attract $+q$ if $Q_1$ is negative, or repel it if $Q_1$ is positive
• Similarly, $Q_2$ must either attract or repel depending on its sign

Let’s assume both $Q_1$ and $Q_2$ are positive: Then both repel $+q$, and the forces are in opposite directions. For net force to be zero, the magnitudes must be equal. Since $P$ is closer to $Q_2$, the force due to $Q_2$ would naturally be stronger unless its charge is smaller. So, to balance, $Q_2$ must have smaller magnitude than $Q_1$. Therefore, the charges are of the same sign, and since $P$ is closer to $Q_2$, for forces to cancel, we must have: 

$|Q_1| > |Q_2|$ 

Answer: (D) $Q_1$ and $Q_2$ have the same sign, but magnitude of $Q_1$ is greater than the magnitude of $Q_2$