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A cylindrical conductor of radius R carries a uniform charge per unit length λ.

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Question: 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)?

Options:

  1. 0
  2. λ/(2πε₀r)
  3. λ/(2πε₀R)
  4. λ/(4πε₀r²)

Correct Answer: λ/(2πε₀r)

Solution: 

For a point outside the cylinder, the electric field is given by E = λ/(2πε₀r).

A cylindrical conductor of radius R carries a uniform charge per unit length λ.

Practice Questions

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)?
  1. 0
  2. λ/(2πε₀r)
  3. λ/(2πε₀R)
  4. λ/(4πε₀r²)

Questions & Step-by-Step Solutions

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)?
  • 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.
  • Electric Field of a Charged Cylinder – The electric field outside a uniformly charged cylindrical conductor can be derived using Gauss's law, which states that the electric field at a distance r from the axis is inversely proportional to r.
  • Gauss's Law – A fundamental principle in electromagnetism that relates the electric flux through a closed surface to the charge enclosed by that surface.
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