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A load is positioned at "r" distance toward the centre of a conductor sphere, with the...

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A load is positioned at "r" distance toward the centre of a conductor sphere, with the radius R, set on the ground. Find the load induced on sphere.

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1) The first alternative:r>R

The sphere, because is set on the ground, has a nul potential everywhere, including inside of it. The induced loads, q', on the sphere's surface, no matter teir distribution on sphere, they give in the sphere's centre the total potential

q'/(4*pi*epsilon*R)

This potential compund with the one produced by the load q, has to be nul.

q'/(4*pi*epsilon*R) + q/(4*pi*epsilon*r)=0, so

q'=-q*R/r

2) The second alternative: r<R

The potential of the sphere being nul and having outside spherical symmetry, that means that the induced load q', along with the load q, o matter it's position, has to be nul, so q'=-q

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