How Can You Find the Energy Densities of an Electromagnetic Wave?

[bon]

Homework Statement

Find the energy densities of an electromagnetic wave separately for the contribtions arising from the electric and magnetic field components

Homework Equations

The Attempt at a Solution

How does one do this?

Is it just the usual derivation for a continuous charge distribution and then the one for a uniform current etc?

Is there a good website with this on that anyone can point me in the direction of? Thanks!

 

[bon]

Another quick question:

SO it then asked me to work out the ratio of the energy denstities, which i did:

mu 0 times e0 times E^2/B^2

But then it says: find the characteristic impedence, defined as the ratio E/H of free space...

does this follow from what I've just done? If so, howwww?

 

[bon]

anyone?

 

[tiny-tim]

hi bon!

(have a mu: µ and an epsilon: ε and try using the X² and X₂ icons just above the Reply box )

… the ratio of the energy denstities, which i did:

mu 0 times e0 times E^2/B^2

But then it says: find the characteristic impedence, defined as the ratio E/H of free space...

in free space, B = µ₀H

 

[bon]

Thanks but I am still not sure how to get to the answer:

the ratio of the energy denstities is µε E²/B²

so substituting B=µH I get

the ratio to be (ε/µ) E²/H²...but this still doens't allow me to get E/H -! This just tells me the ratio of the energy densities..

 

[bon]

hi bon!

(have a mu: µ and an epsilon: ε and try using the X² and X₂ icons just above the Reply box )


in free space, B = µ₀H

Sorry I thought id quote you just so you see that I've replied!

 

[tiny-tim]

you can also use E/B = c

Sorry I thought id quote you just so you see that I've replied!

but i get an email notification anyway

 

[bon]

you can also use E/B = c


but i get an email notification anyway

Aha ok thanks!

And sorry - i didnt realize you get an email notification :)

Thanks again.

 

[L-x]

Homework Statement

Find the energy densities of an electromagnetic wave separately for the contribtions arising from the electric and magnetic field components

Are you still having trouble with this? there's a very neat way to do it using conservation of energy.

Begin by writing down a relationship between du/dt , div N and Jf.E for some volume dV, if you're unsure of the origin of the J.E term consider the work done dW by fields in moving some charge ro dV by dl.

Once you have the relationship, start with J.E and manipulate it using maxwell's equations until you have a term that looks like div N and some other terms. Those other terms will be du/dt.

you will need to use the identity div (AxB)= A.curl B - B.curl A

u is energy density, Jf free current and ro is a charge density