# Work done by the electric field

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1. Oct 2, 2014

### JimBeans

Apologies in advance if this question seems trivial, I seem to have missed something conceptually and would like some clarification.
If an electric field from a point charge does work on another charge and thereby loses energy, where does the lost energy come from?
It is my understanding that the energy in the electric field is directly proportional to the magnitude of the point charge from which it comes. Does this mean when the electric field does work, the point charge effectively loses charge?
To me that seems to make no sense, so if anyone could clarify I would appreciate it.

2. Oct 3, 2014

### sweet springs

Hi. Electric field working on a charge is coming not from that charge but from other charges. Via electric field the charge and other charges interact and energy and mometum transfer occurs.

Charge does not change but distances between charges tend to change to lose or store energy in the fields.

Last edited: Oct 3, 2014
3. Oct 3, 2014

### Redbelly98

Staff Emeritus
Welcome to Physics Forums!

A charged object does not lose charge simply by doing work (i.e. attracting or repelling) another charged object, since total charge must be conserved. You're intuition is correct that losing charge makes no sense.

I'll give an example shortly. There are two things to keep in mind: (1) the energy stored in "the electric field" is stored in the combined field of all charged objects, not in the field of just one object or the other. (2) the energy density due to the field is proportional to the square of the electric field magnitude.

So, imagine two positively charged objects, relatively close to each other and initially at rest. They repel each other and, as time goes on, they get further apart. Work is done on each object by the field of the other, and both objects gain kinetic energy due to that work.

Now we can ask, how does the field, and the energy stored in the field, change as the charged objects separate? In the vicinity of the charges, the field gets weaker as the charges move farther apart. With the field energy depending on the square of the field magnitude, we find -- when we do the math -- that the total stored energy has decreased.

Hope that makes sense -- I did skip some details, such as doing the math explicitly, not knowing how much calculus you have covered in school yet. If you have covered volume integrals in a multi-variable calc course, we could get more into those details if you like.

Last edited: Oct 3, 2014
4. Oct 3, 2014

### JimBeans

Thanks for the replies. I think the fault in my reasoning may have been that I only considered the effect of one charge on the other.
I have done multi-variable calculus, if you have time i'd like to see the details.
Thanks again.