# Capacitance of an isolated spherical conductor

• Supernova123
In summary: Self_capacitanceNo they are with respect to infinity. To find them you need to integrate the electric field from the surface of the sphere to infinity.Otherwise every charged particle free in empty space would have capacitance.
Supernova123
So it says here that a conducting sphere of radius R with a charge Q uniformly distributed over its surface has V = Q/4πεR , using infinity as the reference point having zero potential,,V (∞) = 0. This gives C = Q/|ΔV| = Q/(Q/4πεR)=4πεR. Does ,V (∞) mean that you are taking the potential of a sphere of infinitely large radius and compressing it into a sphere of radius R to find V? Sorry if my understanding is completely wrong, haha. But why is the potential difference equated to ,V (∞) - V? Also, assuming that the sphere is charged to a potential V1. A spark then occurs which discharges the sphere to a potential V2. Would the energy of the spark be E=c(V1-v2)^2/2 or E=c((V1)^2-(V2)^2)/2 ? I'm confused about the potential difference part. Thank's for your time!

If it is truly isolated, there is no capacitance. There is also no way to define the voltage. Voltage is always measured as a difference between two points. Similarly, capacitance is caused by opposite charges on two or more nearby objects. That excludes isolated objects.

So your puzzle about the Q and V goes away is there is no V.

anorlunda said:
If it is truly isolated, there is no capacitance. There is also no way to define the voltage. Voltage is always measured as a difference between two points. Similarly, capacitance is caused by opposite charges on two or more nearby objects. That excludes isolated objects.

So your puzzle about the Q and V goes away is there is no V.
I thought that the potential of the object was the work done in bringing a unit charge from infinity.

Thst is the potential difference between the object and the reference value at infinity. You may assume the voltage at infinity is zero, or any other reference value. There is no such thing as absolute voltage.

In capacitance, it is the proximity of two objects which is the origin of capacitance, so the proximity is central to the concept, not incidental,

Oops, that was a typo sorry. What I meant was insulated spherical conductor.

anorlunda said:
Thst is the potential difference between the object and the reference value at infinity. You may assume the voltage at infinity is zero, or any other reference value. There is no such thing as absolute voltage.

In capacitance, it is the proximity of two objects which is the origin of capacitance, so the proximity is central to the concept, not incidental,
I see your argument, but the following link describes the capacitance of an isolated sphere: http://hyperphysics.phy-astr.gsu.edu/hbase/electric/capsph.html#c2
Another example is the Hertzian Dipole, where the end plates have much more capacitance than calculated by the parallel plate formula. They seem to act as isolated plates having quite large self capacitance.

tech99 said:
I see your argument, but the following link describes the capacitance of an isolated sphere: http://hyperphysics.phy-astr.gsu.edu/hbase/electric/capsph.html#c2
Another example is the Hertzian Dipole, where the end plates have much more capacitance than calculated by the parallel plate formula. They seem to act as isolated plates having quite large self capacitance.

I looked at the link you provided. It appears that they implicitly assume that the sphere sits above a ground plane. The voltages in the formulas are with respect to ground. In my definition, that's not isolated. Otherwise every charged particle free in empty space would have capacitance.

Re The Herzian Dipole: I really can't speak about RF frequencies, antennas, or the impedance of free space. I'll bow to your knowledge on that.

anorlunda said:
I looked at the link you provided. It appears that they implicitly assume that the sphere sits above a ground plane.
I see no such thing over there.
The voltages in the formulas are with respect to ground. In my definition, that's not isolated.
No they are with respect to infinity. To find them you need to integrate the electric field from the surface of the sphere to infinity.
Otherwise every charged particle free in empty space would have capacitance.
I really don't see the problem with this. It's true that the self-capacitance can be ignored in most cases.

The sphere is surrounded by a conducting sphere at infinite distance. We're not talking about large values of capacitance, the self-capacitance of the Earth is just 700uF.

Scroll down to Self-Capacitance here: http://en.m.wikipedia.org/wiki/Capacitance

## What is the capacitance of an isolated spherical conductor?

The capacitance of an isolated spherical conductor is a measure of its ability to store electrical charge. It is defined as the ratio of the charge on the conductor to the potential difference across it.

## What factors affect the capacitance of an isolated spherical conductor?

The capacitance of an isolated spherical conductor is affected by its radius, the dielectric constant of the material surrounding it, and the distance between the conductor and any surrounding conductors or surfaces.

## How is the capacitance of an isolated spherical conductor calculated?

The capacitance of an isolated spherical conductor can be calculated using the formula C = 4πε0r, where C is the capacitance, ε0 is the permittivity of free space, and r is the radius of the conductor.

## What is the unit of capacitance for an isolated spherical conductor?

The unit of capacitance for an isolated spherical conductor is farads (F). One farad is equal to one coulomb of charge per volt of potential difference.

## Can the capacitance of an isolated spherical conductor be changed?

Yes, the capacitance of an isolated spherical conductor can be changed by altering its radius, the dielectric material surrounding it, or the distance between the conductor and any surrounding conductors or surfaces. It can also be changed by applying an external electric field.

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