Shaskolskaya & Eltsin Problem 229

Physics

Problem

If a ball is surrounded with a concentric metal sphere, an induced charge will appear on the inner surface of the sphere equal in magnitude, but opposite in sign, to the charge of the ball; as a result there will be a charge of the same magnitude and of the same sign as the ball's charge on the external surface of the sphere. This will create the same electric field in the space outside as the ball was creating before. Both the ball and the sphere act in the same way as a charge concentrated at the centre of the ball; therefore the force acting on the piece of paper will remain unaltered. If the paper is surrounded by the sphere, the force of attraction will be reduced to zero: the paper will be in a Faraday's cylinder, a charge appearing on the sphere, but there being no field inside the sphere. The metal sphere will be attracted to the ball, but not the paper.

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