Why Do Spherical Capacitors Have Equal and Opposite Charges?

In summary, when a constant voltage is applied to a spherical capacitor with a metal sphere and outer metal shell, the two plates will have the same total charge due to the conservation of charge. This is because if one plate receives a positive charge (+Q), the other plate must receive a negative charge (-Q) in order to maintain a balance. This is possible because the two conductors are connected, allowing for a flow of charge between them.
  • #1
center o bass
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If you have a spherical capacitor consisting of a metal sphere at an inner radius and an outer metal shell at an outer radius.. then you apply a constant voltage over the two plates.

Why is it so that the two metal plates will have the same total charge? Is this by conservation of charge?

Im thinking that it might be because if +Q goes to one sphere and charge can not be created, so therefore -Q has to go to the other? Is this correct?
 
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  • #2
I think I was a bit too fast posting this question :)
I figured it must be because the two conductors are connected such that a current of charge runs from the one to the others. Hence -Q goes to one leaving the other with +Q.
 

FAQ: Why Do Spherical Capacitors Have Equal and Opposite Charges?

What is a spherical capacitor with charge Q?

A spherical capacitor with charge Q is a type of electrical component that consists of two concentric spherical conductors, with one carrying a positive charge Q and the other carrying an equal and opposite negative charge. It is used to store and release electrical energy.

How does a spherical capacitor with charge Q work?

A spherical capacitor with charge Q works by using the electric field created by the two charged spheres to store and release electrical energy. When a voltage is applied, the positive and negative charges are attracted to each other, creating a potential difference between them. This potential difference allows the capacitor to store energy, which can then be released when needed.

What is the formula for calculating the capacitance of a spherical capacitor with charge Q?

The formula for calculating the capacitance of a spherical capacitor with charge Q is C = 4πε0r, where C is the capacitance, ε0 is the permittivity of free space, and r is the radius of the spheres.

What factors affect the capacitance of a spherical capacitor with charge Q?

The capacitance of a spherical capacitor with charge Q is affected by several factors, including the distance between the spheres, the size of the spheres, and the dielectric material between the spheres. Additionally, the charge on the spheres and the voltage applied also impact the capacitance.

What are the applications of a spherical capacitor with charge Q?

A spherical capacitor with charge Q has several applications in electronics, including as a component in power supplies, filters, and oscillators. It is also used in medical equipment, such as X-ray machines, and in scientific research for precise measurements of electric fields.

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