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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 doubled, what happens to the electric field at the surface?

Options:

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

Correct Answer: It remains the same

Solution: 

The electric field due to a uniformly charged infinite cylinder depends only on the charge per unit length, not on the radius.

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 doubled, what happens to the electric field at the 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 radius of the cylinder is doubled, what happens to the electric field at the surface?
  • Step 1: Understand that we have a cylindrical Gaussian surface that encloses a charge Q.
  • Step 2: Recognize that the electric field around a charged object depends on the charge and the distance from the charge.
  • Step 3: Note that for a cylindrical charge, the electric field is determined by the charge per unit length (Q/L) and not the radius of the cylinder.
  • Step 4: Realize that if we double the radius of the cylinder, the charge per unit length remains the same because the total charge Q is unchanged.
  • Step 5: Conclude that since the electric field depends only on the charge per unit length, the electric field at the surface of the cylinder does not change when the radius is doubled.
  • Gauss's Law – The electric field around a charged object can be determined using Gauss's Law, which states that the electric flux through a closed surface is proportional to the enclosed charge.
  • Electric Field of a Cylinder – The electric field due to an infinitely long charged cylinder is determined by the charge per unit length and is independent of the radius of the cylinder.
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