What is the electric field at a distance r from a uniformly charged disk of radius R and surface charge density σ?
Practice Questions
1 question
Q1
What is the electric field at a distance r from a uniformly charged disk of radius R and surface charge density σ?
σ/(2ε₀)
σ/(4ε₀)
σ/(2ε₀) * (1 - r/√(R² + r²))
Zero
The electric field at a distance r from a uniformly charged disk is given by E = σ/(2ε₀) * (1 - r/√(R² + r²)).
Questions & Step-by-step Solutions
1 item
Q
Q: What is the electric field at a distance r from a uniformly charged disk of radius R and surface charge density σ?
Solution: The electric field at a distance r from a uniformly charged disk is given by E = σ/(2ε₀) * (1 - r/√(R² + r²)).
Steps: 6
Step 1: Understand the problem. We want to find the electric field (E) at a distance (r) from a disk that has a uniform charge spread over its surface.
Step 2: Identify the variables. The radius of the disk is R, and the surface charge density (amount of charge per area) is σ.
Step 3: Recall the formula for the electric field due to a uniformly charged disk. The formula is E = σ/(2ε₀) * (1 - r/√(R² + r²)).
Step 4: Break down the formula. The term σ/(2ε₀) represents a constant factor based on the charge density and a constant (ε₀ is the permittivity of free space).
Step 5: Understand the term (1 - r/√(R² + r²)). This part adjusts the electric field based on the distance (r) from the disk and the radius (R) of the disk.
Step 6: Plug in the values for σ, R, and r into the formula to calculate the electric field at that specific distance.
