# Help with Mathematical Description & Calculations of Space Charge Density

• Buzzer33
In summary, the space charge density of the point charge is described by the delta function, and the potential is calculated for lines E field that intersect the point charge.
Buzzer33
Homework Statement
leaarning
Relevant Equations
no
Guys I have Problems with this task The arrangement consists of a point charge Q at a distance (x0, y0,0) from the origin and two perfectly conductive surfaces in the (x, z) and (y, z) plane

a) Mathematical description of the space charge density p of the original and mirror charge using the delta function. Consider the perfectly conductive surfaces as infinitely extended in the respective direction and carry out reflections. b) Calculate the potential

c) Draw lines E field

Has somebody ideas for a)and b) because I am learning currently

Here the sketch to the task

https://ibb.co/zbSyb3d

Buzzer33 said:
Homework Statement:: leaarning
Relevant Equations:: no

Guys I have Problems with this task The arrangement consists of a point charge Q at a distance (x0, y0,0) from the origin and two perfectly conductive surfaces in the (x, z) and (y, z) plane

a) Mathematical description of the space charge density p of the original and mirror charge using the delta function. Consider the perfectly conductive surfaces as infinitely extended in the respective direction and carry out reflections. b) Calculate the potential

c) Draw lines E field

Has somebody ideas for a)and b) because I am learning currently

Here the sketch to the task

https://ibb.co/zbSyb3d
Welcome to PF.

The picture of your sketch is pretty fuzzy, but it looks like it is a single point charge that is located a distance awat from two orthogonal conducting planes? If you have a better picture or can post an image of the actual problem statement, that would help.

Also, you need to show your work before we can offer tutorial help.

And what do you know about the E-field lines for a point charge above a single conducting plane? What does it mean to use a "mirror charge" image, and how does that simplify the problem?

I made the sketch a little better .I haven't got a better on .

I did a little work in b) which is in the pic but don't know what to do further

https://ibb.co/0CqtSqY

Buzzer33 said:
I made the sketch a little better .I haven't got a better on .

I did a little work in b) which is in the pic but don't know what to do further

View attachment 289170

https://ibb.co/0CqtSqY
I can't read the LHS of the equation, but the RHS looks right for the space charge density of the point charge.
Please post algebra as typed in, not in images (per forum rules). Use LaTeX if you can. There's a guide at the link at bottom left.

What about the mirror charges? Where are they, and what are their signs?
Hint: it's very like looking at your own reflections in two mirrors at right angles.

berkeman
Last edited by a moderator:
Buzzer33 said:
Do you know how to draw line E field ?

https://ibb.co/6DxjK2W
The diagram at that link looks good. Doesn't that do it for you?

## 1. What is space charge density?

Space charge density is a measure of the electric charge per unit volume in a given region of space. It is typically denoted by the symbol ρ and is expressed in units of coulombs per cubic meter (C/m³).

## 2. How is space charge density calculated?

Space charge density can be calculated by dividing the total electric charge in a given volume by the volume itself. Mathematically, it is expressed as ρ = Q/V, where ρ is the space charge density, Q is the total charge, and V is the volume.

## 3. What is the significance of space charge density?

Space charge density plays a crucial role in understanding the behavior of electric fields and the movement of charged particles in a given region of space. It is also important in the design and operation of electronic devices, as it can affect their performance and efficiency.

## 4. How does space charge density relate to electric potential?

Space charge density and electric potential are directly related through the equation ρ = ε∇²φ, where ε is the permittivity of the material and φ is the electric potential. This relationship helps to determine the electric field and potential distribution in a given space.

## 5. Can space charge density be negative?

Yes, space charge density can be negative. This usually occurs when there is an excess of negative charges in a given region, resulting in a negative value for ρ. It is important to note that the sign of space charge density does not affect its physical significance, only the direction of the electric field it produces.

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