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
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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.

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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.
 

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