What is the electric field due to a uniformly charged infinite plane sheet?
Practice Questions
1 question
Q1
What is the electric field due to a uniformly charged infinite plane sheet?
0
σ/2ε₀
σ/ε₀
σ/4ε₀
According to Gauss's law, the electric field due to an infinite plane sheet with surface charge density σ is E = σ/2ε₀, directed away from the sheet.
Questions & Step-by-step Solutions
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Q
Q: What is the electric field due to a uniformly charged infinite plane sheet?
Solution: According to Gauss's law, the electric field due to an infinite plane sheet with surface charge density σ is E = σ/2ε₀, directed away from the sheet.
Steps: 6
Step 1: Understand that we are dealing with an infinite plane sheet that has a uniform charge on it.
Step 2: Know that the surface charge density is represented by the symbol σ (sigma). This tells us how much charge is on a certain area of the sheet.
Step 3: Recall Gauss's law, which relates the electric field to the charge enclosed by a surface.
Step 4: For an infinite plane sheet, we can use a Gaussian surface (like a cylinder) that intersects the sheet.
Step 5: Calculate the electric field using Gauss's law, which gives us the formula E = σ/2ε₀, where ε₀ (epsilon naught) is the permittivity of free space.
Step 6: Note that the electric field E is directed away from the sheet if the charge is positive, and towards the sheet if the charge is negative.
