gives the electric field at points near a charged conducting surface. By applying this equation to a conducting sphere of radius r, carrying charge q on its surface, we will show that the electric field outside the sphere is the same as the field of a point charge at the position of the centre of the sphere.

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We will use the result that the electric field at points near the surface of a charged conductor is given by

Let us consider a conducting sphere of radius r, carrying a charge q on its surface. The surface charge density on the conducting sphere will be

By using the result , we note that the electric field at points near the surface of the spherical conductor will be

This is the same as the electric field outside the sphere of radius r due to a point charge q located at the centre.