What is the electric field at a point due to a uniformly charged infinite plane
Practice Questions
Q1
What is the electric field at a point due to a uniformly charged infinite plane sheet? (2020)
0
σ/2ε₀
σ/ε₀
σ/4ε₀
Questions & Step-by-Step Solutions
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.
