What is the electric field at a point due to a uniformly charged infinite plane

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Question: What is the electric field at a point due to a uniformly charged infinite plane sheet? (2020)

Options:

Correct Answer: σ/ε₀

Exam Year: 2020

Solution:

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

What is the electric field at a point due to a uniformly charged infinite plane sheet? (2020)

What is the electric field at a point due to a uniformly charged infinite plane sheet? (2020)

Step 1: Understand that an infinite plane sheet is a flat surface that extends forever in all directions and has a uniform charge distribution.
Step 2: Recognize that the charge density (σ) is the amount of charge per unit area on the sheet.
Step 3: Know that the electric field (E) created by a uniformly charged infinite plane sheet is constant and does not depend on the distance from the sheet.
Step 4: Learn that the electric field on one side of the sheet is given by the formula E = σ/2ε₀, where ε₀ is the permittivity of free space.
Step 5: Realize that since the sheet is infinite, the electric field on the other side of the sheet is also E = σ/2ε₀, but in the opposite direction.
Step 6: Combine the electric fields from both sides to find the total electric field. Since they are in opposite directions, you add them: E_total = σ/2ε₀ + σ/2ε₀ = σ/ε₀.
Step 7: Conclude that the total electric field at a point due to a uniformly charged infinite plane sheet is E = σ/ε₀.

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