Question

Two point charges \( +3 \, \mu C \) and \( +8 \, \mu C \) repel each other with a force of 40 N. If a charge of \( -5 \, \mu C \) is added to each of them, then the force between them will become:

• A. \( -10 \, \text{N} \)
• B. \( +10 \, \text{N} \)
• C. \( +20 \, \text{N} \)
• D. \( -20 \, \text{N} \)

Hint:

When charges of opposite signs are added to each other, the force can change its direction and magnitude based on the new charge configuration.

Answer 1

The Correct Option is B

Step 1: Use Coulomb's Law.
The force between two charges is given by Coulomb's law: \[ F = \frac{k q_1 q_2}{r^2} \] where \( k \) is Coulomb's constant, \( q_1 \) and \( q_2 \) are the charges, and \( r \) is the distance between them.

Step 2: Apply the new charges.
When \( -5 \, \mu C \) is added to each charge, the new charges become \( -2 \, \mu C \) and \( +3 \, \mu C \). Substituting these into Coulomb’s law, the new force is: \[ F_{\text{new}} = \frac{k (-2 \, \mu C)(3 \, \mu C)}{r^2} = 10 \, \text{N} \]