Spherical Capacitors: Large Radii & Close Together

[gracy]

I thought any two concentric conducting spheres of radii a and b such that a<b form a spherical parallel plate capacitor.But according to my book
A spherical capacitor behaves as a parallel plate capacitor if it's spherical surfaces have large radii and are close to each other.
1)it's spherical surfaces have large radii
2)and are close to each other.
I don't understand how can these two be true at the same time?
I mean if spherical surfaces will be close to each other they won't have larger radii.

 

[cnh1995]

The spheres should indeed be close to each other but I don't see why they should be large. Perhaps because larger surface area will increase the capacitance.

 

[Dale]

Gracy, this is a problem that you should try to work out on your own first. Write down the equation of a spherical capacitor and a parallel plate capacitor. Take some limits and see if you can get it to look like eaach other.

 

[sophiecentaur]

I don't understand how can these two be true at the same time?

Draw a large circle and then draw a very slightly smaller concentric circle. Isn't the distance between them small, yet are the circles not large? Why should 1. and 2. be mutually exclusive?
I think you often ask questions before giving yourself time to work out the answers yourself. PF may go into Gracy-question fatigue and you may not get answers to a question that is seriously important to you.

 

[litup]

I thought it was just area V area kind of thing, X amount of capacitance with X amount of area of conductors, times the dielectric constant. It would seem to me a nested sphere would give the same capacitance area for area as two square 2 D plates. If you have a paper capacitor, two conductive layers separated by an insulator, say paper, if you bend those surfaces into a curve, the capacitance won't change very much at all, perhaps a little bit since maybe some of the paper may get a bit squished and therefore the conductive layers closer at a bend or something but outside of that, if you had a capacitance meter hooked up measuring the resultant capacitance it would read the same whether it was laid out flat or all crumpled up in a mess.
Maybe there would be inductive effects of being curved, not sure about that. Here is a link about parasitic inductance in capacitors:
http://www.capacitorguide.com/parasitic-inductance/

 

[sophiecentaur]

I thought it was just area V area kind of thing, X amount of capacitance with X amount of area of conductors, times the dielectric constant. It would seem to me a nested sphere would give the same capacitance area for area as two square 2 D plates. If you have a paper capacitor, two conductive layers separated by an insulator, say paper, if you bend those surfaces into a curve, the capacitance won't change very much at all, perhaps a little bit since maybe some of the paper may get a bit squished and therefore the conductive layers closer at a bend or something but outside of that, if you had a capacitance meter hooked up measuring the resultant capacitance it would read the same whether it was laid out flat or all crumpled up in a mess.

Yes. As long as the ratio of the radii is near unity, you could slit them like an orange peel and re-assemble them as to nearly identical flat plates and the effective areas would be near enough the same. The outside sphere would have a bit left over so the capacitance would be a bit less. It is trivial to work out the areas of the inner and outer spheres and it would be the difference that would affect the capacitance.

all crumpled up in a mess.

In practice, crumpling the thing up would probably affect the spacing, which really could have a significant effect; more than any area change.

 

[gracy]

The spheres should indeed be close to each othe

But isolated/single spherical capacitor has it's other plate (sphere) at infinity.

 

[cnh1995]

But isolated/single spherical capacitor has it's other plate (sphere) at infinity.

How so? I haven't seen anything like that. Plates close to each other ensure uniform electric field between them. So the plates have to be close to each other.

 

[SammyS]

But isolated/single spherical capacitor has it's other plate (sphere) at infinity.

This is very different from the situation you refer to in your OP.

 

[ehild]

But isolated/single spherical capacitor has it's other plate (sphere) at infinity.

There are spherical capacitors, and there are isolated spheres. An isolated conductive sphere has capacitance but we do not use isolated spheres as capacitors. They would need too big space. You certainly remember, that a sphere of radius 9000000 km has 1 F capacitance. Capacitors of 1 μF capacitance are quite common, in case of an isolated sphere its radius would be 9 km.