Problem:
A charge q is kept at a distance of 2R from the centre of a grounded conducting sphere of radius R. What is the image charge and its distance from the centre of the sphere?

Solution:
To solve this problem, we will use the method of image charges.

Understanding the Problem:
We have a charge q placed at a distance of 2R from the centre of a grounded conducting sphere. The conducting sphere is neutralized by grounding, meaning that it acquires an equal and opposite charge to that of the charge q. Our goal is to find the image charge and its distance from the centre of the sphere.

Method of Image Charges:
The method of image charges is a technique used to solve electrostatic problems involving conductors and charges. It involves introducing a fictitious charge, called an image charge, to simplify the problem. The image charge is chosen in such a way that it satisfies the boundary conditions of the problem.

Steps to Solve:
1. Determine the charge acquired by the conducting sphere due to grounding. Since the sphere is grounded, it acquires an equal and opposite charge to that of the charge q. Therefore, the charge acquired by the sphere is -q.
2. Place an image charge, denoted as q', inside the sphere at a distance of 2R from its centre. The image charge is chosen in such a way that it cancels the electric field inside the conducting sphere due to the charge q.
3. Determine the distance of the image charge from the centre of the sphere. Since the image charge is placed at a distance of 2R from the centre of the sphere, its distance from the centre is 2R.

Conclusion:
The image charge is -q and its distance from the centre of the sphere is 2R. By introducing the image charge, we have simplified the problem by considering the conducting sphere as an isolated charged object. This method allows us to determine the electric field and potential at any point outside the sphere.