Why doesn't a stationary electron lose energy by radiating electric field (as per coulomb's law)? 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?
 A: 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.
A: 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.
A: 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.
