# Parallel Conducting plates problem

• ajmaeen
In summary, if two parallel conducting plates with surface areas of 1msq each are placed at a small distance apart and one plate is given a charge of +Q while the other remains neutral, the outer sides of both plates will have a charge of 0, while the inside will have a charge of +Q and -Q. The field will only exist in the middle of the plates. If only one plate has an excess charge, there will be four unknown surface charges that can be solved for using equations based on the total charge in each plate and the absence of a field inside either plate.
ajmaeen
If we have two parallel conducting plates ( of surfaces 1msq each), set at a very small distance apart, so that the plates can be considered like infinite plates (no edge effect).

Both plates are neutral at first.

Now a charge (say +Q) is placed on one of the plates. the other still is neutral

What will be the charge on each face of both the plates, and the field at A, B and C, where A is outer side of plate 1, B is middle of plate 1 and 2, and C in outer side of plate 2?

My thoughts:
i know that if the other plate also had an opposite excess charge then on the outer sides charges are 0 , while inside they would be +Q and -Q. so field would also only exist in the middle.

but I am a but confused on what it should be incase of only one plate with the excess charge?

Create unknowns for the four surface charges. You can immediately write down two equations based on knowing the total charge in each plate. Since there is no field inside either plate, you can develop two more equations.

## 1. What is the Parallel Conducting Plates problem?

The Parallel Conducting Plates problem is a common problem in electrostatics where two parallel conducting plates with opposite charges are placed in an electric field. The problem involves calculating the electric potential, electric field, and charge distribution between the plates.

## 2. What is the significance of the Parallel Conducting Plates problem?

The Parallel Conducting Plates problem is significant because it is a fundamental problem in electromagnetics and helps in understanding the behavior of electric fields and conductors. It also has practical applications in the design of capacitors and other electronic devices.

## 3. How is the Parallel Conducting Plates problem solved?

The Parallel Conducting Plates problem can be solved using the method of images, where the two plates are replaced by a set of point charges with opposite signs. Another approach is using the method of separation of variables, where a series solution is obtained for the electric potential between the plates.

## 4. What are the boundary conditions for the Parallel Conducting Plates problem?

The boundary conditions for the Parallel Conducting Plates problem are that the electric field is perpendicular to the surface of the plates and is continuous across the boundary. Additionally, the electric potential is constant on the surface of each plate.

## 5. What are some real-world applications of the Parallel Conducting Plates problem?

The Parallel Conducting Plates problem has many real-world applications, such as in the design of capacitors, which are used in electronic circuits for energy storage. It is also important in understanding the behavior of parallel-plate capacitors in high voltage power transmission systems. Additionally, the problem has applications in electrostatic painting, electroplating, and electrochemical processes.

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