Understanding Electric Field of Positive & Negative Plates

AI Thread Summary
The confusion arises from the calculation of the electric field due to positive and negative plates. The electric field from a single plate is given by E = σ/(2ε₀), not σ/ε₀. When considering both plates, the total electric field is indeed the sum of the contributions from each plate, resulting in E = σ/ε₀. Using a pillbox Gaussian surface helps clarify this concept. Understanding these principles resolves the initial confusion regarding the electric field's magnitude.
annamal
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Homework Statement
Two large conducting plates carry equal and opposite charges, with a surface charge density as shown in image. The separation between the plates is d. What is the
electric field between the plates?
Relevant Equations
##\vec E = \frac{\sigma}{\epsilon_0}##
I am confused with the solution. It says ##\vec E = \frac{\sigma}{\epsilon_0}##. Shouldn't E = ##2*\vec E = 2*\frac{\sigma}{\epsilon_0}##? Electric field of the positive plate and electric field of the negative plate.

Screen Shot 2022-04-25 at 11.02.53 PM.png
 
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annamal said:
I am confused with the solution. It says ##\vec E = \frac{\sigma}{\epsilon_0}##. Shouldn't E = ##2*\vec E = 2*\frac{\sigma}{\epsilon_0}##?
It should not. Use a pillbox Gaussian surface with one flat face inside the conductor and the other flat face in the vacuum to see why and become unconfused.
 
Well if you mean that the total E-field should be double of that of the one plate, yes that is true but the field of one plate is ##E=\frac{\sigma}{2\epsilon_0}##. So the total field is $$2\frac{\sigma}{2\epsilon_0}=\frac{\sigma}{\epsilon_0}$$
 
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