Point charge in a conducting plane

In summary, a point charge in a conducting plane is a situation where a single electric charge is placed near a conducting surface. Due to the presence of the conducting plane, the electric field lines are distorted and the charge experiences a force towards the surface. This phenomenon is known as image charge and can be calculated using the method of images. The resulting force on the charge is perpendicular to the surface and can be used to analyze the behavior of charges in similar situations. This concept is important in understanding the behavior of electric fields near conductors and has various applications in physics and engineering.
  • #1
sami23
76
1
Point charge +Q is placed close to a very large conducting plane. A professor of physics asserted that the field caused by this configuration is the same as would be obtained by removing the plane and placing a point charge -Q of equal magnitude in the mirror-image position behind the initial position of the plane. Is this correct? Why or why not?
 
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  • #2
It is correct. The method of placing mirror charges is an easy way to solve such problems.
Experience tells you were to put the charges.
The mathematical way to see this, is by solving the Poisson equation using the correct boundary conditions for the Green function.
 
  • #3
betel said:
It is correct. The method of placing mirror charges is an easy way to solve such problems.
Experience tells you were to put the charges.
The mathematical way to see this, is by solving the Poisson equation using the correct boundary conditions for the Green function.


Does the voltage of the plane matter?
 
  • #4
thedore said:
Does the voltage of the plane matter?

What do you mean by voltage? A single plane can not have a voltage, you have to specify in relation to what the voltage is considered. But you can have a charge on the plane.
 
  • #5
thedore said:
Does the voltage of the plane matter?

Yes,the plane must be grounded

And the mathematical principle behind such "cheating" solution is http://en.wikipedia.org/wiki/Uniqueness_theorem" .
 
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  • #6
Actually you want to refer to the theory of images. The plane does not have to be grounded but it cannot have a net charge and it must be infinite in size.

The principle is simple. Electric field lines are perpendicular to a conducting plane. If you mirror the charges on two sides of an imaginary plane (reverse the sign of the charges on opposite sides of the plane) the electric field lines will be perpendicular to the imaginary plane. So mirrored charges produce the same field as charges in front of a mirror. That's how "mirroring" gets it's name.
 
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Related to Point charge in a conducting plane

1. What is a point charge in a conducting plane?

A point charge in a conducting plane refers to a situation where a single charged particle is placed on a flat, conductive surface. This charge can either be positive or negative, and it will induce charges on the surface of the conducting plane.

2. How does a point charge in a conducting plane affect the electric field?

A point charge in a conducting plane will create an electric field that is perpendicular to the surface of the plane. This electric field is strongest directly above or below the point charge, and it decreases in strength as you move further away from the charge.

3. What is the relationship between the charge on the point charge and the induced charges on the conducting plane?

The magnitude of the induced charges on the conducting plane is equal to the magnitude of the point charge. However, the signs of the induced charges will be opposite to the sign of the point charge. This creates an overall neutral charge on the conducting plane.

4. How does the distance between the point charge and the conducting plane affect the electric field?

The strength of the electric field is inversely proportional to the distance between the point charge and the conducting plane. This means that as the distance increases, the electric field strength decreases.

5. What is the difference between a point charge in a conducting plane and a point charge in free space?

In a conducting plane, the presence of the charged surface affects the electric field of the point charge. This results in a different distribution of charges compared to a point charge in free space, where there are no external influences on the electric field.

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