Question

Two point charges \(+3\) C and \(+6\) C separated by a distance 'r' , repel each other with a force of 27 N. If each of the above charges is given an additional charge of \(-5\) C, the force experienced by them is

• A. \(6\text{N}\) (attractive)
• B. \(6\text{N}\) (repulsive)
• C. \(3\text{N}\) (attractive)
• D. \(3\text{N}\) (repulsive)

Hint:

Find k over r squared from the first situation, then recompute the net charges and force.

Answer 1

The Correct Option is C

Step 1: Understanding the Concept
Coulomb force is \(F=\dfrac{kq_1q_2}{r^2}\), repulsive for like charges and attractive for unlike charges.

Step 2: Initial situation
\(\dfrac{k\cdot3\cdot6}{r^2}=27\Rightarrow\dfrac{k}{r^2}=1.5\)

Step 3: New charges
Adding \(-5\text{ C}\) to each gives \(3-5=-2\text{ C}\) and \(6-5=+1\text{ C}\).

Step 4: New force
\(F=1.5\times2\times1=3\text{ N}\), and unlike charges attract.

Final Answer:
The force becomes \(3\text{ N}\) and attractive. \[ \boxed{\text{(C) }3\text{N}\text{ (attractive)}} \]