Question

If it takes an amount of work W to move two +q point charges from infinity to a distance d apart from each other, then how much work should it take to move three +q point charges from infinity to a distance d apart from each other?

(a) 2W.

(b) 3W.

(c) 4W.

(d) 6W.

Short answer

The correct answer is option (b)\(3W\).

Step-by-step solution

Understanding the work done to bring charge from an infinite distance

The work done required to carry a unit charge from infinity to a specific point in space is called electric potential.

The expression for electric potential is,

\(V = \frac{W}{q}\)

Here,Wis the work done andq is the charge.

Given Data

The work done to two charged from infinity to distance d apart is\(W\).

The point charges are \( + q\).

Evaluation of the work needed to move three point charges

In order to bring two point charges from infinity to a distanced, the work done is W. If you put the third charge, it will be repelled by the other two point charges.So, the work done will be\(2W\)to bring the third charge. Hence, the total work done on three point charges is\(3W\).

Thus, the correct option is (b).