Question

Two point charges, \(+2C\) and \(+6C\) repel each other with a force of \(12\)N. If a charge of \((-4C)\) is given to each of these charges, the force now is

• A. \(4\)N, repulsive
• B. \(4\)N, attractive
• C. \(12\)N, attractive
• D. \(8\)N, repulsive

Hint:

Add the new charge to each, then apply Coulomb's law with the same distance.

Answer 1

The Correct Option is B

Step 1: Understanding the Concept
Coulomb's force is \(F=\frac{kq_1q_2}{r^{2}}\), and the distance is unchanged.

Step 2: Initial Condition
\(\frac{k(2)(6)}{r^{2}}=12\), so \(\frac{k}{r^{2}}=1\).

Step 3: New Charges
\(2-4=-2\) C and \(6-4=2\) C, which are opposite in sign.

Step 4: Calculation
\(F'=\frac{k(2)(2)}{r^{2}}=4\times 1=4\) N, and unlike charges attract, so option (B).

Final Answer:
The force is 4 N and it is attractive. \[ \boxed{\text{(B) }\text{4 N, attractive}} \]