What Is the Electric Field Inside a Solenoid with Time-Varying Current?

[VVS]

Hello,

I am trying to find out the electric field inside a solenoid if a time varying current is passed through.
However I am stuck with these partial differential equations.
View attachment Electric field solenoid.pdf
Somehow I can't solve them and I think something is wrong.
Because according to equation (13) the electric field will vary with frequency sigma/epsilon.
However when looking at equation (11) the electric field must be varying with the frequency of the magnetic field, which is arbitrary.
I am really confused.
Does anybody know the answer?

thanks
VVS

 

[SteliosVas]

Your picture doesn't appear, if you check the picture you uploaded is there than I can be sure to help out

 

[davenn]

Your picture doesn't appear, if you check the picture you uploaded is there than I can be sure to help out

there is no pic ... it's a link to a PDF file to open and it works OK :)


Dave

 

[VVS]

So does nobody have an answer to my question?

 

[SteliosVas]

So does nobody have an answer to my question?

Since you have a time varying current, the electromagnetic field created by the solenoid varies with time. The electromagnetic 'news' travels at the speed of light though. You use the quasi-static approximation

 

[Baluncore]

If the solenoid is wound with a perfect conductor, and in free space,
then the ratio of the electric field to the magnetic field will be the intrinsic impedance of free space.
Z_fs= 4*10^-7 * Pi * c = 376.73 ohm