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A cylindrical Gaussian surface of length L and radius R encloses a charge Q. Wha

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Question: A cylindrical Gaussian surface of length L and radius R encloses a charge Q. What is the electric field E at a distance R from the axis of the cylinder?

Options:

  1. Q/(2πε₀R)
  2. Q/(4πε₀R²)
  3. Q/(ε₀L)
  4. 0

Correct Answer: Q/(2πε₀R)

Solution: 

Using Gauss\'s law, the electric field E at a distance R from the axis of a long charged cylinder is E = Q/(2πε₀L) for points outside the cylinder.

A cylindrical Gaussian surface of length L and radius R encloses a charge Q. Wha

Practice Questions

Q1
A cylindrical Gaussian surface of length L and radius R encloses a charge Q. What is the electric field E at a distance R from the axis of the cylinder?
  1. Q/(2πε₀R)
  2. Q/(4πε₀R²)
  3. Q/(ε₀L)
  4. 0

Questions & Step-by-Step Solutions

A cylindrical Gaussian surface of length L and radius R encloses a charge Q. What is the electric field E at a distance R from the axis of the cylinder?
Correct Answer: E = Q/(2πε₀L)
  • Step 1: Understand that we have a cylindrical Gaussian surface with a charge Q inside it.
  • Step 2: Recognize that the electric field E we want to find is at a distance R from the axis of the cylinder.
  • Step 3: Recall Gauss's law, which states that the electric flux through a closed surface is equal to the charge enclosed divided by the permittivity of free space (ε₀).
  • Step 4: For a long charged cylinder, the electric field is uniform and points radially outward from the axis.
  • Step 5: Set up the Gaussian surface: a cylinder of length L and radius R that surrounds the charged cylinder.
  • Step 6: Calculate the electric flux through the curved surface of the Gaussian cylinder, which is E times the surface area (2πRL).
  • Step 7: According to Gauss's law, set the electric flux equal to the enclosed charge divided by ε₀: E(2πRL) = Q/ε₀.
  • Step 8: Solve for the electric field E: E = Q/(2πε₀L).
  • Step 9: Conclude that this formula gives the electric field E at a distance R from the axis of the cylinder for points outside the cylinder.
  • Gauss's Law – The relationship between electric flux through a closed surface and the charge enclosed by that surface.
  • Electric Field of a Cylinder – Understanding how to calculate the electric field around a cylindrical charge distribution.
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