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

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Question: A cylindrical Gaussian surface encloses a charge Q. If the height of the cylinder is doubled while keeping the radius constant, what happens to the electric flux through the curved surface?

Options:

  1. It doubles
  2. It halves
  3. It remains the same
  4. It becomes zero

Correct Answer: It doubles

Solution: 

The electric flux through the curved surface is proportional to the charge enclosed, which remains constant, so the flux through the curved surface doubles if the height is doubled.

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

Practice Questions

Q1
A cylindrical Gaussian surface encloses a charge Q. If the height of the cylinder is doubled while keeping the radius constant, what happens to the electric flux through the curved surface?
  1. It doubles
  2. It halves
  3. It remains the same
  4. It becomes zero

Questions & Step-by-Step Solutions

A cylindrical Gaussian surface encloses a charge Q. If the height of the cylinder is doubled while keeping the radius constant, what happens to the electric flux through the curved surface?
Correct Answer: Electric flux through the curved surface doubles.
  • Step 1: Understand that electric flux is related to the charge enclosed by a surface.
  • Step 2: Recognize that the charge Q inside the cylindrical Gaussian surface does not change when the height is doubled.
  • Step 3: Know that the electric flux through the curved surface of the cylinder is given by the formula: Flux = Electric Field (E) × Area (A).
  • Step 4: The area of the curved surface of a cylinder is calculated as: Area = 2πrh, where r is the radius and h is the height.
  • Step 5: If the height (h) of the cylinder is doubled, the new area of the curved surface becomes: New Area = 2πr(2h) = 4πrh, which is double the original area.
  • Step 6: Since the electric field (E) remains constant (as the charge enclosed is constant), the electric flux through the curved surface also doubles because Flux = E × New Area.
  • Gauss's Law – The electric flux through a closed surface is proportional to the charge enclosed within that surface.
  • Electric Flux – Electric flux is defined as the product of the electric field and the area through which it passes, and it is affected by the geometry of the surface.
  • Cylindrical Symmetry – In cylindrical coordinates, the electric field due to a point charge or a line charge can be analyzed using cylindrical Gaussian surfaces.
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