Chapter 23, Problem 1FTD

Two positive point charges are infinitely far apart. Is it possible, using a finite amount of work, to move them until they’re a small distance d apart?

To determine

Whether finite work be enough to bring two positive charges together.

Answer to Problem 1FTD

Finite work is enough for bringing to positive charges together.

Explanation of Solution

Let there be two positive charges which are infinitely far away from each other.

Since both of them are positive charges the work done to bring them is positive since energy is supplied to the system.

Write the equation to find the electrostatic work done to bring two charges together.

$W=k\frac{q_1{q}_2}{r}$

Here,

$W$ is the work done.

$q_1$ is the charge of first positive charge.

$q_2$ is the charge of second charge.

$r$ is the distance between charges.

Here the charges are infinitely far away. So by replacing the distance by infinity work done becomes zero which is a finite quantity.

Therefore finite work can bring two positive charges together from infinite distance.

Conclusion:

Finite work is enough for bringing to positive charges together.