Prove that the electric field outside a charged solitary conducting ball is the same as the field of a point charge in its center?

Since the surface of the conductor is equipotential, the lines of the electric field of the charged conducting ball leave the surface of the ball perpendicular to it. If the charge on the surface of the ball is q, then the electric field outside the ball is the same as the field of a point charge q located in the center of the conducting ball.

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