A cylindrical conductor of radius R carries a uniform charge per unit length λ. What is the electric field at a distance r from the axis of the cylinder (r > R)?
Practice Questions
1 question
Q1
A cylindrical conductor of radius R carries a uniform charge per unit length λ. What is the electric field at a distance r from the axis of the cylinder (r > R)?
0
λ/(2πε₀r)
λ/(2πε₀R)
λ/(4πε₀r²)
For a point outside the cylinder, the electric field is given by E = λ/(2πε₀r).
Questions & Step-by-step Solutions
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Q
Q: A cylindrical conductor of radius R carries a uniform charge per unit length λ. What is the electric field at a distance r from the axis of the cylinder (r > R)?
Solution: For a point outside the cylinder, the electric field is given by E = λ/(2πε₀r).
Steps: 5
Step 1: Understand that we have a cylindrical conductor with a radius R and it carries a uniform charge per unit length, denoted as λ.
Step 2: Identify the point where we want to find the electric field, which is at a distance r from the axis of the cylinder, where r is greater than R (r > R).
Step 3: Recall that for a long, straight charged cylinder, the electric field outside the cylinder behaves like that of a point charge.
Step 4: Use the formula for the electric field E at a distance r from a line of charge, which is E = λ / (2πε₀r).
Step 5: Conclude that this formula gives us the electric field at the specified distance from the axis of the cylinder.
