How would you Calculate the Energy in an EM field?

[Ryan Reed]

How would you calculate the energy in an electromagnetic field produced by a particle such as an electron?

 

[Vanadium 50]

I'd square it. Energy density is E² times a constant depending on your units. Then integrate over all space. Of course you get infinity.

 

[Ryan Reed]

But as it goes out, the energy would get smaller and smaller, getting to the point where even though it's infinite, the energy would be so much smaller the farther you go away, it couldn't reach the next decimal place. Think about it like this, a circle with certain dimensions will have a definite volume, even though numbers are infinitely dividable and if you add the radius each time you change the angle until you get to 360 degrees, it will be infinity since 360 can be divided infinitely, but this doesn't happen.

 

[davenn]

But as it goes out, the energy would get smaller and smaller, getting to the point where even though it's infinite, the energy would be so much smaller the farther you go away,

have you heard of the inverse square law ?
do a google search and have a read

 

[Stephen Tashi]

A related old thread: https://www.physicsforums.com/threads/the-energy-of-a-point-charge.232921/

 

[Vanadium 50]

I don't know what to say. Integrals take care of this. That's why we use them,

 

[Ryan Reed]

I don't know what to say. Integrals take care of this. That's why we use them,

What I mean by this is the answer should be something like pi, infinitely long, not infinitely large. Pi is infinitely long, but will never go above 3.14

 

[Vanadium 50]

I know that's what you meant. This whole conversation has an Alice-In-Wonderland aspect, with you - who doesn't know how to do the integral - telling me - who does - that he is wrong, based on your feelings. That's why I don't know what to say.

 

[jtbell]

But as it goes out, the energy would get smaller and smaller, getting to the point where even though it's infinite, the energy would be so much smaller the farther you go away,

Try going in the other direction, closer and closer to the charge. If the charge is a mathematical point with zero size, what happens?

 

[Dale]

But as it goes out,

What do you mean "as it goes out"? The E field of a charge does not radiate energy, it stores energy. The energy that is there does not go anywhere without a B field also.

As was pointed out earlier, the self energy of a classical point charge is infinite, but it does not radiate.