# Finding Charge Density on the Surface of a Slab

• LulaBell
In summary, the conversation discusses an attempt at solving a physics problem involving an infinite sheet of charge and a conducting slab. The problem asks for the charge density on the surface of the slab at a specific point. The person is experiencing difficulty with their solution, as it is giving them a power ten error and their answer does not match the given charge densities. They mention trying an answer of 3.15 μC/m2, but it is also incorrect.
LulaBell
Homework Statement
An infinite sheet of charge is located in the y-z plane at x = 0 and has uniform charge density σ1 = 0.31 μC/m2. Another infinite sheet of charge with uniform charge density σ2 = -0.32 μC/m2 is located at x = c = 22 cm. An uncharged infinite conducting slab is placed halfway in between these sheets ( i.e., between x = 9 cm and x = 13 cm).

What is σa, the charge density on the surface of the conducting slab at x = 9 cm?
Relevant Equations
E infinite slab = σ/2Eo
Here's my attempt at a solution, but when I plug it in, it gives me a power ten error. I don't really understand what I'm doing wrong here. I think all my variables are in the correct units and it asks for my answer to be in μC/m2. Any help is much appreciated.

LulaBell said:
Homework Statement:: An infinite sheet of charge is located in the y-z plane at x = 0 and has uniform charge density σ1 = 0.31 μC/m2. Another infinite sheet of charge with uniform charge density σ2 = -0.32 μC/m2 is located at x = c = 22 cm. An uncharged infinite conducting slab is placed halfway in between these sheets ( i.e., between x = 9 cm and x = 13 cm).

What is σa, the charge density on the surface of the conducting slab at x = 9 cm?
Relevant Equations:: E infinite slab = σ/2Eo

Here's my attempt at a solution, but when I plug it in, it gives me a power ten error. I don't really understand what I'm doing wrong here. I think all my variables are in the correct units and it asks for my answer to be in μC/m2. Any help is much appreciated.

View attachment 322397
You don't say what your final answer is. It should be obvious it will be similar in magnitude to the two given charge densities.

MatinSAR
My final answer was 3.15 * 10^-7 which was wrong so I thought maybe it was supposed to be 3.15 uC/m^2 but that was wrong as well.

LulaBell said:
My final answer was 3.15 * 10^-7 which was wrong so I thought maybe it was supposed to be 3.15 uC/m^2 but that was wrong as well.
Neither of those is the same order of magnitude as the two given charge distributions, so must be wrong.

## What is charge density, and how is it defined on the surface of a slab?

Charge density is a measure of electric charge per unit area on a surface. On the surface of a slab, it is defined as the amount of electric charge per unit area (σ) and is typically measured in coulombs per square meter (C/m²). It is calculated by dividing the total charge (Q) by the surface area (A) of the slab.

## How can Gauss's Law be used to find the charge density on the surface of a slab?

Gauss's Law states that the electric flux through a closed surface is proportional to the enclosed charge. To find the charge density on the surface of a slab, one can construct a Gaussian surface that encloses part of the slab's surface. By calculating the electric flux and knowing the permittivity of the medium, the surface charge density can be determined from the relationship between flux and enclosed charge.

## What is the relationship between electric field and surface charge density for a slab?

The electric field (E) just outside the surface of a slab with surface charge density (σ) is related by the equation E = σ / ε₀, where ε₀ is the permittivity of free space. This relationship assumes a uniform charge distribution and that the field is perpendicular to the surface.

## How do boundary conditions affect the determination of surface charge density on a slab?

Boundary conditions are crucial in determining surface charge density because they dictate how the electric field behaves at the interface of different materials. For a slab, the continuity of the perpendicular component of the electric field across the boundary helps in calculating the surface charge density. Discontinuities in the electric field can indicate the presence of surface charges.

## What methods can be used to experimentally measure the surface charge density on a slab?

Experimental methods to measure surface charge density on a slab include using an electrometer to measure surface potential, employing a Faraday cup to collect and measure charge, and using non-contact methods like Kelvin probe force microscopy (KPFM) to map surface potential and infer charge density. These methods provide quantitative data on the charge distribution on the slab's surface.

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