What is the electric field due to a uniformly charged infinite plane sheet with

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Question: What is the electric field due to a uniformly charged infinite plane sheet with surface charge density σ?

Options:

Correct Answer: 2σ/ε₀

Solution:

The electric field due to an infinite plane sheet is E = σ/2ε₀ on both sides, thus total E = σ/ε₀.

What is the electric field due to a uniformly charged infinite plane sheet with surface charge density σ?

What is the electric field due to a uniformly charged infinite plane sheet with surface charge density σ?

Step 1: Understand that we have an infinite plane sheet that is uniformly charged. This means the charge is spread out evenly over the surface.
Step 2: Identify the surface charge density, denoted by σ. This is the amount of charge per unit area on the sheet.
Step 3: Recall that the electric field (E) created by an infinite plane sheet with surface charge density σ is given by the formula E = σ/2ε₀, where ε₀ is the permittivity of free space.
Step 4: Note that this electric field points away from the sheet on both sides of it. Therefore, there is an electric field of σ/2ε₀ on one side and another σ/2ε₀ on the opposite side.
Step 5: To find the total electric field in the region between the two sides of the sheet, you add the two electric fields together: E_total = σ/2ε₀ + σ/2ε₀.
Step 6: Simplify the total electric field: E_total = σ/ε₀.

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