Finding Charge Density on the Surface of a Slab

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.
  • #1
LulaBell
3
0
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.

IMG_1550.jpg
 
Physics news on Phys.org
  • #2
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.
 
  • Like
Likes MatinSAR
  • #3
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.
 
  • #4
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.
Your 35593.22N/C is wrong.
 

1. What is charge density on the surface of a slab?

Charge density on the surface of a slab refers to the amount of charge per unit area on the surface of a slab. It is a measure of how much charge is distributed on the surface of the slab.

2. How is charge density on the surface of a slab calculated?

Charge density on the surface of a slab is calculated by dividing the total charge on the surface of the slab by the surface area of the slab. The formula is Q/A, where Q is the total charge and A is the surface area.

3. What factors affect the charge density on the surface of a slab?

The charge density on the surface of a slab is affected by the amount of charge present on the surface, the surface area of the slab, and the material properties of the slab such as its dielectric constant and conductivity.

4. How does the charge density on the surface of a slab impact its electric field?

The charge density on the surface of a slab determines the strength of the electric field on the surface. A higher charge density leads to a stronger electric field, while a lower charge density results in a weaker electric field.

5. How is the charge density on the surface of a slab used in practical applications?

The charge density on the surface of a slab is an important factor in determining the behavior of materials in various applications such as capacitors, batteries, and electronic devices. It is also used in the study of electrochemistry and surface chemistry.

Similar threads

Charge Density on a Conductive Slab
    • Introductory Physics Homework Help
Replies
1
Views
2K
E&M: Gauss' Law Surface Charge Density
    • Introductory Physics Homework Help
Replies
4
Views
504
I Thought I Understood Gauss' Law (Sheets)
    • Introductory Physics Homework Help
Replies
26
Views
590
Surface Current and Electric Field
    • Introductory Physics Homework Help
Replies
1
Views
744
Relationship between radial distance and charge density of a capacitor
    • Introductory Physics Homework Help
Replies
2
Views
1K
Induced charge density at the interface of dielectric slabs
    • Introductory Physics Homework Help
Replies
3
Views
2K
Charge on inner/outer surfaces of two large parallel conducting plates
    • Introductory Physics Homework Help
Replies
11
Views
400
E-field of solid sphere with non-uniform charge density
    • Introductory Physics Homework Help
Replies
3
Views
1K
Semi-infinite slab of charges -- find E and charge density
    • Introductory Physics Homework Help
Replies
8
Views
2K
Variable induced surface charge density on a sphere
    • Introductory Physics Homework Help
Replies
9
Views
2K

Hot Threads

Recent Insights

Back
Top