# Is there an equation that proves that Energy is always Conserved?

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Enclose a positively charged sphere in neutral concentric spheres as shown in the image. Connect outer surface A to Earth, inner A to outer B, inner B to outer C and finally inner C to the central sphere. These spheres are good electric conductors and are insulated from one another.

When you discharge a charged body using the laws of conservation of energy the electric energy of the current that flows is equal to the energy you put in charging the body, the description shows that on top of Earthing the system we can still get more electric energy flowing in different parts of the system due to the presence of the same charge. So little electric potential energy in the central sphere say 10J is giving rise to say 100J electric energy flow.

Will I get more electric energy flowing than the electrostatic potential energy stored in the central Sphere?

Edited by Maximillian

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Is there an equation that proves that Energy is always Conserved?

Connect outer surface A to Earth, inner A to outer B, inner B to outer C and finally inner C to the central sphere. These spheres are good electric conductors and are insulated from one another.

That doesn't make sense. You say they are connected to one another but that they are insulated from one another.

When you discharge a charged body using the laws of conservation of energy the electric energy of the current that flows is equal to the energy you put in charging the body, the description shows [/size]that on top of Earthing the system we can still get more electric energy flowing in different parts of the system due to the presence of the same charge. So little electric potential energy in the central sphere say 10J is giving rise to say 100J electric energy flow.

What is the basis for this claim?

You can't show that conservation of energy is violated by just making up numbers.

Will I get more electric energy flowing than the electrostatic potential energy stored in the central Sphere?[/size]

No.

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Equal charged particles spread on surface randomly in equal distances each other.
But area of your spheres A, B and C is slightly different, because radius is different.

Area of sphere A,B,C:
$A_A=4 \pi r_A^2$

$A_B=4 \pi r_B^2$

$A_C=4 \pi r_C^2$

Charge C per each surface area m2:
$C_A=\frac{C_0}{A_A}$

$C_B=\frac{C_0}{A_B}$

$C_C=\frac{C_0}{A_C}$
(if they have charge C0 equal in each sphere)

Or:

$C=\frac{C_A}{A_A}$

$C=\frac{C_B}{A_B}$

$C=\frac{C_C}{A_C}$
(if they have charge per surface area equal, but charge per sphere has to be different)

Edited by Sensei

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*assuming time translation symmetry

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I agree with Strange +1

When you do this please consider what happens to the charge when it arrives at 'Earth' - shell A?

'There is a conservation of charge law'

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To answer the title question: no, an equation doesn't prove anything, experiments do.

However, despite many, many attempts, not a single experiment has ever been performed where conservation of energy was violated.

Edited by Bender

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To answer the title question: no, an equation doesn't prove anything, experiments do.

However, despite many, many attempts, not a single experiment has ever been performed where conservation of energy was violated.

Well not quite true as some experiments where this occured in regards to particle decays indicated we were missing something as the conservation of energy was violated by the experiment. This in turn made us realize their must be another interaction going on. But directly testing conservation of energy itself showed no violations Edited by Mordred

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Conservation of energy seemed to be violated

Out of curiosity: are you referring to the formation neutrino's?

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mediator bosons in general with various conservation laws

Edited by Mordred

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The conservation of energy shows up in the equations of what ever it is your equating. Energy manifests itself in different ways, heat, light, kinetic etc. Therefore there is no equation for generic energy, conserved or not. Hope this helps