Finding Charge Density on the Surface of a Slab

Click For Summary
SUMMARY

The discussion focuses on calculating the surface charge density (σa) on an infinite conducting slab placed between two charged sheets. The first sheet has a charge density of σ1 = 0.31 μC/m², and the second has σ2 = -0.32 μC/m². The user encountered errors while attempting to compute σa, specifically a power ten error, and received feedback indicating that their final answers were not in the correct order of magnitude. The relevant equation for electric field due to an infinite slab, E = σ/2ε₀, was highlighted as crucial for solving the problem.

PREREQUISITES
  • Understanding of electric fields generated by charged sheets
  • Familiarity with the concept of charge density (σ) in μC/m²
  • Knowledge of the equation E = σ/2ε₀ for infinite slabs
  • Basic proficiency in unit conversions and scientific notation
NEXT STEPS
  • Review the principles of electrostatics related to infinite charge distributions
  • Learn about the behavior of electric fields in the presence of conductors
  • Practice problems involving charge density calculations using E = σ/2ε₀
  • Explore common errors in unit conversions and scientific notation in physics
USEFUL FOR

This discussion is beneficial for physics students, particularly those studying electrostatics, as well as educators and tutors assisting with charge density calculations and electric field concepts.

LulaBell
Messages
3
Reaction score
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
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.
 
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.
Your 35593.22N/C is wrong.
 

Thread 'Magnitude of buoyant force in fluids of different densities'

The book claims the answer is that all the magnitudes are the same because "the gravitational force on the penguin is the same". I'm having trouble understanding this. I thought the buoyant force was equal to the weight of the fluid displaced. Weight depends on mass which depends on density. Therefore, due to the differing densities the buoyant force will be different in each case? Is this incorrect?
View full post »

Similar threads

Charge Density on a Conductive Slab
  • · Replies 1 ·
Replies
1
Views
3K
E&M: Gauss' Law Surface Charge Density
  • · Replies 4 ·
Replies
4
Views
1K
Induced charge density at the interface of dielectric slabs
  • · Replies 3 ·
Replies
3
Views
3K
Find the density of surface charges at the boundary of two conductors with different resistivities
  • · Replies 6 ·
Replies
6
Views
1K
Relationship between radial distance and charge density of a capacitor
  • · Replies 2 ·
Replies
2
Views
2K
Surface Current and Electric Field
  • · Replies 1 ·
Replies
1
Views
2K
I Thought I Understood Gauss' Law (Sheets)
  • · Replies 26 ·
Replies
26
Views
3K
Induction heat flux density induced by wire in a slab
  • · Replies 0 ·
Replies
0
Views
984
Semi-infinite slab of charges -- find E and charge density
  • · Replies 8 ·
Replies
8
Views
3K
E-field of solid sphere with non-uniform charge density
  • · Replies 3 ·
Replies
3
Views
2K