What Is the Correct Sign for the Capacitance of a Spherical Capacitor?

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In summary, the capacitance of a spherical conductor with radius 1 and charge -Q inside another larger spherical conductor with radius 2 and charge +Q at the inside surface is found using Gauss' law to determine the electric field between the two conductors. This is then integrated with respect to r to find the change in potential, which is then divided by Q to calculate the capacitance. The resulting value is always positive and can be expressed as 8*pi*Eo, where Eo is a constant."
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Say you have a spherical conductor with radius 1 with charge -Q inside of another larger spherical conductor(with radius 2 to the inside edge of the conductor)with a charge +Q at the inside surface, what's the capacitance?

I used Gauss' law to find E in between the two conductors, then integrated with respect to r to find the change in potential, and did Q/that=C

I'm pretty sure I got the right actual answer, it was like 8*pi*Eo...and maybe something else(Eo is that constant), I don't remember off hand(this was on a test I took this morning)but my question...should it be positive or negative? That really confused me and I had all kinds of negatives floating around and finally fixed it up so that C came out positive, and it looked like it made sense
 
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Capacitance is always a positive value. Is that what you mean?
 
  • #3
it is? Good then, that's what I figured at the time, but I got to thinking afterwards
 

FAQ: What Is the Correct Sign for the Capacitance of a Spherical Capacitor?

What is a spherical capacitor?

A spherical capacitor is a type of electrical capacitor that consists of two conductive spheres separated by a dielectric material. It is used to store electric charge and has applications in various electrical circuits.

How does a spherical capacitor work?

A spherical capacitor works by creating an electric field between the two conductive spheres. When a voltage is applied, one sphere becomes positively charged while the other becomes negatively charged. The dielectric material between the spheres helps to increase the capacitance of the capacitor.

What is the capacitance of a spherical capacitor?

The capacitance of a spherical capacitor is determined by the size of the spheres, the distance between them, and the dielectric constant of the material between them. It can be calculated using the formula C = (4πε0εr) / d, where ε0 is the permittivity of free space, εr is the relative permittivity of the dielectric material, and d is the distance between the spheres.

How is a spherical capacitor different from other types of capacitors?

A spherical capacitor differs from other types of capacitors in its shape and construction. It has two conductive spheres instead of parallel plates and uses a dielectric material between them instead of air or vacuum. This allows for a higher capacitance and more efficient storage of charge.

What are the applications of a spherical capacitor?

Spherical capacitors have several applications in electrical circuits, including in power supplies, filters, and timing circuits. They are also used in scientific research and experiments, such as in high-voltage testing and particle accelerators.

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