A point charge `q_(0)` is moved slowly from the centre of a ring R, ( that is carrying a charge q) to a distance x from its centre along its axis. What is the work done by the external agent in this process ?
Strategy `:` According to work energy theorem, if there is no change in kinetic energy, we have
`W_(ext)+ W_(E ) = 0`
`implies W _(ext) = - W_(E )`
`= - q_(0)(V_(A)-V_(B))`

Explanation

To solve the problem of finding the work done by the external agent when moving a point charge \( q_0 \) from the center of a ring carrying charge \( q \) to a distance \( x \) from its center along its axis, we can follow these steps:

### Step 1: Understand the System
We have a ring of radius \( R \) with a total charge \( q \) uniformly distributed along it. A point charge \( q_0 \) is moved from the center of the ring (point A) to a point along the axis of the ring at a distance \( x \) (point B).

### Step 2: Apply Work-Energy Theorem
According to the work-energy theorem, if there is no change in kinetic energy, we have:
\[
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