What Are the E and B Fields Inside a Capacitor Within a Solenoid?

[cool4u224]

Homework Statement

Consider a large solenoid aligned with the z-axis with a uniform magnetic field inside given by Bo = Boz[hat]. Contained WITHIN the solenoid is a very large parallel plate capacitor and the plates (one at the x=0 plane and the other at the x = d plane) have surface charge densities of +σo (plate at x=0) and -σo (plate at x=d). Assume that the fields well within the capacitor are uniform.

A) Sketch the fields inside the capacitor. That is, show E and B. Given that the solenoid have no loops per unite length, what current, I0, must be run through he solenoid to produce the magnetic field strength of Bo?

Homework Equations

For a solenoid B = 0 outside and B = μ_onI inside

The Attempt at a Solution

I am having trouble getting expressions for the E and B fields inside the capacitor. If I can get a little bit of help on this I think I can answer the rest of the questions pertaining to this problem.

 

[vela]

Homework Statement

Consider a large solenoid aligned with the z-axis with a uniform magnetic field inside given by Bo = Boz[hat]. Contained WITHIN the solenoid is a very large parallel plate capacitor and the plates (one at the x=0 plane and the other at the x = d plane) have surface charge densities of +σo (plate at x=0) and -σo (plate at x=d). Assume that the fields well within the capacitor are uniform.

A) Sketch the fields inside the capacitor. That is, show E and B. Given that the solenoid have no loops per unite length, what current, I0, must be run through he solenoid to produce the magnetic field strength of Bo?

Homework Equations

For a solenoid B = 0 outside and B = μ_onI inside

The Attempt at a Solution

I am having trouble getting expressions for the E and B fields inside the capacitor. If I can get a little bit of help on this I think I can answer the rest of the questions pertaining to this problem.

Where exactly are you getting stuck?

 

[cool4u224]

I am just confused on where to start. Are their just standard E and B fields within the capacitor? The book we are using is very narrow and has little usage outside of the examples and problems they assign. in this problem I have to go on to find the energy densities of E and B-fields in terms of σ_o and I_o.

 

[vela]

The parallel-plate capacitor is a standard topic in introductory electromagnetics, so I'm sure your book covers it. You can check other books as well if you don't like yours. Or try googling "parallel plate capacitor".

 

[cool4u224]

I realize that the Parallel plate capacitor is a standard topic, but where do they ever discuss one embedded in a solenoid? That is where I am getting caught up. How does, if it does at all, the solenoid affect the E and B fields within the capacitor. Likewise, how does the Capacitor affect the E and B fields withing the Solenoid but outside the Capacitor? Once I figure out an expression for the E and the B fields I think I can get the rest. I am just struggling with that part.
Thanks.

 

[vela]

Books aren't going to discuss every possible configuration. That would be impossible. You need to take what you know about electric and magnetic fields and deduce what E and B should be in this situation. Where do electric fields come from? Magnetic fields?