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If an electron in a universe constantly generates an electric field why does it not get annihilated ? I am confused because I read that an accelerating charge radiates and loses energy. So, why won't a stationary electron radiate and lose energy?

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Where did you read that accelerated charges radiate? In that reference, please look at the derivation, which should answer your question. –  Robert Filter Apr 23 '13 at 11:50
    
Its from the maxwells laws. –  scienceauror Apr 24 '13 at 9:27
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3 Answers

You can think of it this way -

The field isn't being created 'constantly'. That's like saying our hands and legs are being 'created constantly'. The field is coupled to an electric charge, and that's how it is.

When a charge is being accelerated, it is gaining energy (since work is being done on the charge) and it also looses energy (through the radiation). The electrostatic field doesn't have anything to do with this picture. When a charge is static, the field is also static.

In a universe where there is exactly one charge sitting in a vacuum, the charge will have an electric field. But the field does no work, and no work is done on the field. So there is no loss of energy.

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the answer to your question is best seen this way. You know(I presume) that the electromagnetic energy in space is dependent of the elctric and magnetic field present. In this case we only have an electric field that is static, so we know that the charge is not adding any energy to the fields. So, it doesn´t lose energy, even though it is creating a field always.

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"Creating a field always"- itself means its dissipating energy,else how can an electrostatic field exist without energy being stored in it? –  scienceauror Apr 23 '13 at 11:07
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It is because the energy of the electric field around the electron, is potential energy. Potential energy means that given the conditions energy can be extracted from a system. For example two electrons repulse each other, and give each other kinetic energy, calculable from the distance between them.

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So u mean the dissipated energy can be taken back by an electron,and the system exists in an equilibrium between dissipation and absorption of energy? –  scienceauror Apr 23 '13 at 11:05
    
There is no dissipation . The field just is there . It is similar to the potential energy of a lake in a mountain. It just sits there. If a channel down hill appears the water will run and change the potential energy to kinetic energy which then is expended. –  anna v Apr 23 '13 at 11:51
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