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360. Problem 30.64 (RHK) We have to estimate (a) the charge required to raise an isolated metallic sphere of radius 1.0-m radius to a potential of 1.0 MV. (b) We have to estimate the charge required to raise an isolated metallic sphere of radius 1.0-cm to the same amount of potential, 1.0 MV. (c) We have to answer why in an electrostatic accelerator a large metal sphere is deployed when the same potential can be achieved using a smaller charge with a small sphere. |
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Solution: Click For PDF Version Charge required on the surface of a metal sphere of radius R for it to be at potential V is given by the relation
(a) For a metal sphere of radius of 1.0 m to be at a potential of
(b) For a metal sphere of radius of 1.0 cm to be at a potential of
(c) Electric field near a charged metal surface is proportional to its surface charge density. The surface charge density for a 1.0-m metal sphere to be at 1 MV potential, will be
And the surface charge density for a 1.0-cm metal sphere to be at 1 MV potential, will be
Therefore, in order to have not too large electric field near the surface of charged conductor, it is preferred to deploy in electrostatic accelerators a metal sphere of a large radius. |
amount
of charge required will be
