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A cylindrical Gaussian surface encloses a charge Q. If the radius of the cylinde

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Question: A cylindrical Gaussian surface encloses a charge Q. If the radius of the cylinder is r and its height is h, what is the electric flux through the curved surface?

Options:

  1. Q/ε₀
  2. Q/(2ε₀)
  3. Q/(4ε₀)
  4. 0

Correct Answer: Q/ε₀

Solution: 

The electric flux through the curved surface of a cylinder is given by Φ = Q_enc/ε₀, where Q_enc = Q.

A cylindrical Gaussian surface encloses a charge Q. If the radius of the cylinde

Practice Questions

Q1
A cylindrical Gaussian surface encloses a charge Q. If the radius of the cylinder is r and its height is h, what is the electric flux through the curved surface?
  1. Q/ε₀
  2. Q/(2ε₀)
  3. Q/(4ε₀)
  4. 0

Questions & Step-by-Step Solutions

A cylindrical Gaussian surface encloses a charge Q. If the radius of the cylinder is r and its height is h, what is the electric flux through the curved surface?
  • Step 1: Understand that we have a cylindrical Gaussian surface that encloses a charge Q.
  • Step 2: Recognize that the electric flux (Φ) through a surface is related to the charge enclosed (Q_enc) by the formula Φ = Q_enc/ε₀, where ε₀ is the permittivity of free space.
  • Step 3: Since the entire charge Q is enclosed by the cylindrical surface, we set Q_enc = Q.
  • Step 4: Substitute Q_enc into the electric flux formula: Φ = Q/ε₀.
  • Step 5: Note that the formula gives us the total electric flux through the entire surface of the cylinder, but we are specifically interested in the curved surface.
  • Step 6: For a cylindrical surface, the electric field is uniform and perpendicular to the curved surface, so the flux through the curved surface can be calculated using the same formula.
  • Gauss's Law – The relationship between electric flux through a closed surface and the charge enclosed by that surface.
  • Electric Flux – The measure of the quantity of electric field lines passing through a surface.
  • Cylindrical Symmetry – Understanding how electric fields behave in cylindrical geometries.
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