Spherical capacitor with epoxy dielectric and battery voltage

[Alouette]

Homework Statement

There's a spherical capacitor, inner radius a and outer radius b, with a filling in between of epoxy, and also connected to battery of voltage V. What is the capacitance?

Also, what is magnitude of surface charge density outer shell?

Homework Equations

For Q1
1)C=4∏ε₀(ab/b-a)

2)C = Q/ΔV

3)C = κC₀

For Q2
s=Q/4∏r²

The Attempt at a Solution

Used above equation, but it doesn't include any voltage V nor dialelectric constant κ. Are these the right equations?

Haven't attempted Q2 since it seems to require C/m² as units for answer...

 

[darkxponent]

First you show the attempt. Then only we will know how to help

 

[Alouette]

Sure. Except I already did. I said I used C=4∏ε0(ab/b-a) but this gave me the wrong answer. I noticed that it didn't even used V or dialelectric constant κ, but I'm unable to find how these fit it. The only other equations I found involving them were equations 2) and 3).

C = Q/ΔV , this has V but I'm unsure how there's a change in V when they gave me just a constant voltage. Also there wasn't any charge in the question either...

C = κC0, I would have to use the equation 1) C and then multiply by epoxy constant, which I found to be either 3.9, 4.1, or 4.4, not sure which one but I was going to plug them into find out.

 

[Alouette]

4*π*k*ε/((1/a)-(1/b)), where k is 3.6 and ε is 8.85e-12

I don't understand where these equations come from...

the 4πε is from the charge of the sphere?

why the subtraction of inverses?

Not looking for a detailed lecture, just a simple explanation would do to better help me understand the process of arriving at this answer.

 

[gneill]

Do a web search on "spherical capacitor". The Hyperphysics site has some appropriate info.

 

[darkxponent]

seems to me that you are attempting the question without studying the chapter. You don't have a clear idea of what capacitor is. The question you have asked is quite very simple. I don't know how to help you with this question as it is only formula based. I would advice you to first go through the chapter once then only attempt the question