A point charge q is placed at a distance r from the center of an uncharged conducting sphere of radius R (R << r). The potential at any point on the sphere is:

Explanation

When a point charge q is placed at a distance r from the center of an uncharged conducting sphere of radius R (where R < r), the potential at any point on the sphere will be constant and equal to the potential due to the point charge q. The conducting sphere, bring uncharged, initially has an electric potential of zero everywhere on its surface. However, when the charged particle q is brought near the sphere, it induces an opposite charge distribution on the inner surface of the conducting sphere due to electrostatic induction. This induced charge distribution creates an electric field inside the sphere, which cancels out the electric field due to the point charge q at any point inside the conducting sphere. As a result, the electric potential on the inner surface of the conducting sphere becomes constant and equal to the potential due to the point charge q at a distance r from the center of the sphere. The electric potential on the inner surface of the sphere is given by the formula for the electric potential of a point charge: V = k * (q / r) Where: V is the electric potential, k is Coulomb's constant (approximately 8.99 x 10^9 N m^2/C^2), q is the charge of the point charge (in this case, it is q), r is the distance from the point charge to the point on the conducting sphere where the potential is measured. Therefore, the potential at any point on the sphere is given by V = k * (q / r). This potential is constant and equal to the potential due to the point charge q at a distance r from the center of the sphere.