Conservation of energy in electromagnetism?

How is energy conserved in electromagnetism? Is it hinted only from Lenz's law or from Maxwell?

Also, if a solenoid's flow of current produces a magnetic field, and from the magnetic field forces are applied on dipoles, how is energy conserved?

I know that energy is always conserved, but in this case when electric & magnetic fields interact to do work I don't know how to picture conservation.

The way to understand conservation of energy when dealing with electric and magnetic fields is to consider the work they do on charged particles, which leads to a result called Poynting's theorem, see http://www.phy.duke.edu/~rgb/Class/Electrodynamics/Electrodynamics/node33.html.

Electric potential energy, or electrostatic potential energy, is a potential energy (measured in joules) that results from conservative Coulomb forces and is associated with the configuration of a particular set of point charges within a defined system. An object may have electric potential energy by virtue of two key elements: its own electric charge and its relative position to other electrically charged objects.

Lets say you have, two like charges separated by a distance. Like charges repel each other. So, both the charges repel each other. In order to explain this situation in terms of conservation of energy you need to understand that electric charge and relative position of one charge w.r.t other acts as the source of potential energy.

When one charge repels the other charge, it converts the electric potential energy stored into kinetic energy, thus separating the charges. So, law of conservation of energy hols good. Even if you consider the unlike charges, the same explanation can be given that the charges convert their potential energy into kinetic energy thus causing them to come near.

• The reason energy is conserved is because the work done to separate them, is equal to the work required to bring them back to the same position REASON: due to the repulsive force. Assuming there is no repulsive force when work is done to bring them back... conservation of energy does not hold? Im concentrating on the main pillar that holds the law in this case of electric fields and magnetic field, which in this case seems to be the repulsive force(same situation if they we're dipoles) and the their separated distance $r$. – AxtII Feb 19 '14 at 23:27

hard to answer because in this case energy is conserved we all know, but at atomic level. when charged particle moved between charged feilds or between atoms they produces magnetic Fields kinetic energy of the electrons is converted into creating charged fields.

• How can fields contribute to the conservation of energy, knowing that they are conservative? – AxtII Feb 19 '14 at 10:07
• farside.ph.utexas.edu/teaching/em/lectures/node89.html -- in brief!! maybe this helps – Arun Malik Feb 19 '14 at 10:36
• Could you please try to pay attention to punctuation? English is probably not your first language (it isn't mine either), but with some small effort you can greatly improve you posts and make them more readable. – Hunter Feb 20 '14 at 5:31
• why so serious? – Arun Malik Feb 20 '14 at 7:31