Finding Charge Density on the Surface of a Slab

AI Thread Summary
The discussion focuses on calculating the charge density on the surface of a conducting slab placed between two infinite sheets of charge with given densities. The user encounters a power ten error when attempting to solve the problem and is unsure about the accuracy of their variables and units. Another participant points out that the user's final answer is not in the correct order of magnitude compared to the provided charge densities, indicating a potential calculation error. The user also incorrectly calculates the electric field, which contributes to the confusion. Clarification on the correct approach and units is needed to resolve the issue.
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 'Minimum mass of a block'

Thread 'Minimum mass of a block'

Here we know that if block B is going to move up or just be at the verge of moving up ##Mg \sin \theta ## will act downwards and maximum static friction will act downwards ## \mu Mg \cos \theta ## Now what im confused by is how will we know " how quickly" block B reaches its maximum static friction value without any numbers, the suggested solution says that when block A is at its maximum extension, then block B will start to move up but with a certain set of values couldn't block A reach...
View full post »

Thread 'Electric field due to charges between 2 parallel infinite planes'

TL;DR Summary: Find Electric field due to charges between 2 parallel infinite planes using Gauss law at any point Here's the diagram. We have a uniform p (rho) density of charges between 2 infinite planes in the cartesian coordinates system. I used a cube of thickness a that spans from z=-a/2 to z=a/2 as a Gaussian surface, each side of the cube has area A. I know that the field depends only on z since there is translational invariance in x and y directions because the planes are...
View full post »
Thread 'Calculation of Tensile Forces in Piston-Type Water-Lifting Devices at Elevated Locations'

Thread 'Calculation of Tensile Forces in Piston-Type Water-Lifting Devices at Elevated Locations'

Figure 1 Overall Structure Diagram Figure 2: Top view of the piston when it is cylindrical A circular opening is created at a height of 5 meters above the water surface. Inside this opening is a sleeve-type piston with a cross-sectional area of 1 square meter. The piston is pulled to the right at a constant speed. The pulling force is（Figure 2）： F = ρshg = 1000 × 1 × 5 × 10 = 50,000 N. Figure 3: Modifying the structure to incorporate a fixed internal piston When I modify the piston...
View full post »

Similar threads

Charge Density on a Conductive Slab
Replies
1
Views
3K
E&M: Gauss' Law Surface Charge Density
Replies
4
Views
1K
Induced charge density at the interface of dielectric slabs
Replies
3
Views
2K
Find the density of surface charges at the boundary of two conductors with different resistivities
Replies
6
Views
890
Relationship between radial distance and charge density of a capacitor
Replies
2
Views
2K
Surface Current and Electric Field
Replies
1
Views
2K
I Thought I Understood Gauss' Law (Sheets)
Replies
26
Views
2K
Induction heat flux density induced by wire in a slab
Replies
0
Views
808
Semi-infinite slab of charges -- find E and charge density
Replies
8
Views
2K
E-field of solid sphere with non-uniform charge density
Replies
3
Views
2K

Hot Threads

Recent Insights

Back
Top