What is the electric field due to a uniformly charged infinite plane sheet with
Practice Questions
Q1
What is the electric field due to a uniformly charged infinite plane sheet with surface charge density σ?
σ/2ε₀
σ/ε₀
2σ/ε₀
0
Questions & Step-by-Step Solutions
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.
