# What is the surface charge density?

• s0mebody
You can then use the electric field to find the surface charge density on the positive sheet.In summary, the conversation discusses two parallel metal plates with equal and opposite electric charges separated by a distance of 38.0mm. The electric field between them is uniform and has a magnitude of 480 N/C. The potential difference between the plates is 1.824 V, with the positive plate having a higher potential. To find the surface charge density on the positive plate, the electric field due to an infinite sheet of charge can be used, which can be found in most textbooks.
s0mebody

## Homework Statement

Two large parallel metal plate sheets carrying opposite electric charges of equal magnitude are separated by a distance of 38.0mm. The electric field between them is uniform and has magnitude 480 N/C.

a) What is the potential difference between the sheets?
b) Which sheet is at higher potential, the one with positive or negative charge?
c) What is the surface charge density D on the positive sheet?

## The Attempt at a Solution

I have solved a and b.

a) W/q = Potential Difference = Ed = 480(0.0038) = 1.824 V
b) Positive charge

For letter C, I have no idea how do it. It's my first time encountering the term surface charge density on this kind of problem... Pleas help.

Last edited:
Consult your text. I'm sure your book talks about the electric field due to an infinite sheet of charge.

vela said:
Consult your text. I'm sure your book talks about the electric field due to an infinite sheet of charge.

Can you elaborate further? I didn't quite understand.

I'm saying read your textbook. You should know the electric field for three common charge configurations: a point charge, a line charge, and a sheet of charge. Your book will cover these.

The surface charge density is a measure of the amount of electric charge per unit area on the surface of a material. In this case, it refers to the amount of charge per unit area on the surface of the positive sheet.

To find the surface charge density, we can use the formula:

D = Q/A

where D is the surface charge density, Q is the total charge on the sheet, and A is the area of the sheet.

In this problem, we know the electric field between the sheets is 480 N/C. This means that the electric field is equal to the force per unit charge experienced by a test charge placed between the sheets. This test charge can be used to calculate the total charge on the sheet.

F = qE

where F is the force on the test charge, q is the charge of the test charge, and E is the electric field.

In this case, the test charge experiences a force of 480 N. Since the electric field is uniform, the force experienced by the test charge is equal to the force experienced by each unit of charge on the sheet. So we can set F = qE and solve for q:

q = F/E = (480 N)/(480 N/C) = 1 C

This means that the total charge on the sheet is 1 Coulomb.

To find the area of the sheet, we can use the fact that the sheets are parallel and separated by a distance of 38.0mm = 0.038m. This means that each sheet has an area of 0.038m x 0.038m = 0.001444m^2. However, since we are only interested in the positive sheet, we can divide this by 2 to get the area of the positive sheet, which is 0.000722m^2.

Now we can plug in our values to the equation for surface charge density:

D = Q/A = (1 C)/(0.000722m^2) = 1385 C/m^2

So the surface charge density on the positive sheet is 1385 C/m^2.

## 1. What exactly is surface charge density?

Surface charge density is a physical quantity that measures the electric charge per unit area of a surface. It is a measure of the amount of charge present on the surface of a material.

## 2. How is surface charge density different from volume charge density?

Surface charge density only considers the charge present on the surface of a material, while volume charge density takes into account the charge present throughout the entire volume of the material.

## 3. What are the units of surface charge density?

The units of surface charge density are coulombs per square meter (C/m^2) in the SI system of units. In other systems, it can also be expressed as statcoulombs per square centimeter (statC/cm^2) or esu per square centimeter (esu/cm^2).

## 4. How is surface charge density related to electric field?

Surface charge density is directly proportional to the electric field at the surface of a material. This means that as the surface charge density increases, the electric field at the surface also increases.

## 5. What factors affect the surface charge density of a material?

The surface charge density of a material is affected by several factors, including the type of material, its size and shape, the amount of charge present, and the surrounding electric field. It can also be influenced by external factors such as temperature and humidity.

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