Question

Why does multiple charge by induction violate the Law of Energy conservation?

Answer 1

Multiple charges causes different energies

Answer 2

✌✌Hey mate here is your answer ⤵⤵

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Consider 3 hollow conductor spheres A, B and C together with the charged hollow conductor sphere X of charge Q.

Let the spheres A, B, C and X be of a similar capacitance C. i.e.The difference in their capacitances is so small to be significant.

Bring the spheres A, B and C towards X so that the enclose it.

Momentarily earth the spheres A, B, C and X so that A, B and C each gain a net charge Q. Let the volumes of the spheres A, B, C and X each be V. i.e. The difference in their volumes is so small to be significant.

The charge density Z on X was,

Z = Q/V

The charge densities Z on A, B and C are,

Z = Q/V+Q/V+Q/V

Z = 3Q/V

The results show that the charge density of A, B and C charge system is higher than that which was on X.  This is possible because the electrostatic field on the outer most sphere is the vector sum of the electrostatic fields emanating from the charged inner spheres. So the charge density on the outermost sphere is more than that which was on the central sphere if we add the net and induced charges on the surface of the outermost sphere.

Therefore a higher charge density is being created at a certain point in space without as expending energy.

This is compared to crunching a group of like charges together without expending

energy.

This goes against the law of energy conservation.

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✌✌Hope this will help you✌✌