Question

At the three vertices of an equilateral triangle of side \(a\), three point charges are placed (each of \(0.1\,\text{C}\)). If this system is supplied energy at the rate of \(1\,\text{kW}\), calculate the time required to move one of the charges to the mid-point of the line joining the other two. 

• A. \(50\,\text{h}\)
• B. \(60\,\text{h}\)
• C. \(48\,\text{h}\)
• D. \(54\,\text{h}\)

Hint:

Always compute change in electrostatic potential energy, not force, when energy rate is given.

Answer 1

The Correct Option is C

Step 1: Initial potential energy: \[ U_i = 3\frac{kq^2}{a} \]
Step 2: Final distances are \(a/2\) from two charges: \[ U_f = 2\frac{kq^2}{a/2} + \frac{kq^2}{a} \]
Step 3: Change in energy: \[ \Delta U = U_f - U_i \]
Step 4: Time required: \[ t = \frac{\Delta U}{P} \]
Step 5: Substitution gives: \[ t = 48\,\text{h} \]