• Support PF! Buy your school textbooks, materials and every day products via PF Here!

Calculating the charge densities

1. Homework Statement
Lets say you have a infinitely long surface with one side of length ##L## and a surface charge density ##ρ_s## and you need to transform that into a linear charge density ##Q'## so that you can represent the surface along some axis ##y## so the the surface is placed normal to the axis and goes from ##y=0## to ##y=L## how would you make that transition? Take the infinitely long dimension to be ##h##.
2. Homework Equations
3. The Attempt at a Solution

I tried this line of thinking:
$$Q'=\frac{dQ}{dh}=\frac{ρ_sdS}{dh}=\frac{ρ_sdhdl}{dh}=ρ_sdl$$
Could this be correct and how would it be in a more complicated case? Is there a pattern here?
 

haruspex

Science Advisor
Homework Helper
Insights Author
Gold Member
2018 Award
31,384
4,596
I don't understand the arrangement. It is an infinite strip width L, and the y axis is normal to the strip? So say it is L in the x axis and infinite in z. But now you have y from 0 to L? And in what sense are you wanting to "represent" the surface?
 
I don't understand the arrangement. It is an infinite strip width L, and the y axis is normal to the strip? So say it is L in the x axis and infinite in z. But now you have y from 0 to L? And in what sense are you wanting to "represent" the surface?
Sorry, i think i was a little confusing in choosing the words. Lets imagine it like this. You see the wall, the ##y-axis## is to the right and left of this wall, the ##x-axis## is up and down and the ##z-axis## is behind and in front of you. The surface is placed so that it is infinite up and down and of length ##L## from ##y=0## to ##y=L##. Is now clearer?
 

haruspex

Science Advisor
Homework Helper
Insights Author
Gold Member
2018 Award
31,384
4,596
Sorry, i think i was a little confusing in choosing the words. Lets imagine it like this. You see the wall, the ##y-axis## is to the right and left of this wall, the ##x-axis## is up and down and the ##z-axis## is behind and in front of you. The surface is placed so that it is infinite up and down and of length ##L## from ##y=0## to ##y=L##. Is now clearer?
Ok, but then what do you mean by the required transformation into a linear density? Where is this in the picture, and in what sense does it relresent the original charge? The fields are obviously not the same.
 
So with the set up coordinate system you rotate it so that the x-axis looks to you and you see only the z ad the y. The surface looks like a line on the y axis you right? So given the surface charge density can you transform it into a linear charge density along the y axis bu cutting the surface into small elements of ##dy## (lines along the surface). This is the problem.
 

haruspex

Science Advisor
Homework Helper
Insights Author
Gold Member
2018 Award
31,384
4,596
So with the set up coordinate system you rotate it so that the x-axis looks to you and you see only the z ad the y. The surface looks like a line on the y axis you right? So given the surface charge density can you transform it into a linear charge density along the y axis bu cutting the surface into small elements of ##dy## (lines along the surface). This is the problem.
Ok. I think you are asking whether the field in the YZ plane can be simulated by a uniform charge along the Y axis.
The answer is no.
Close to the plane, the field is approximately constant (as for an infinite plane sheet). For a line of charge, the field gets very much stronger as you approach the line.
 

Want to reply to this thread?

"Calculating the charge densities" You must log in or register to reply here.

Related Threads for: Calculating the charge densities

Physics Forums Values

We Value Quality
• Topics based on mainstream science
• Proper English grammar and spelling
We Value Civility
• Positive and compassionate attitudes
• Patience while debating
We Value Productivity
• Disciplined to remain on-topic
• Recognition of own weaknesses
• Solo and co-op problem solving
Top