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A cylindrical Gaussian surface encloses a long straight wire carrying a current.

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Question: A cylindrical Gaussian surface encloses a long straight wire carrying a current. What is the electric field at a distance r from the wire?

Options:

  1. 0
  2. I/(2πε₀r)
  3. λ/(2πε₀r)
  4. σ/(2ε₀)

Correct Answer: 0

Solution: 

Gauss\'s law applies to electric fields, not magnetic fields. The electric field around a current-carrying wire is not defined by Gauss\'s law.

A cylindrical Gaussian surface encloses a long straight wire carrying a current.

Practice Questions

Q1
A cylindrical Gaussian surface encloses a long straight wire carrying a current. What is the electric field at a distance r from the wire?
  1. 0
  2. I/(2πε₀r)
  3. λ/(2πε₀r)
  4. σ/(2ε₀)

Questions & Step-by-Step Solutions

A cylindrical Gaussian surface encloses a long straight wire carrying a current. What is the electric field at a distance r from the wire?
  • Step 1: Understand that we are dealing with a long straight wire that carries an electric current.
  • Step 2: Recognize that the electric field around a current-carrying wire is not the same as the magnetic field.
  • Step 3: Remember that Gauss's law is used to calculate electric fields, but it is not applicable for the electric field around a current-carrying wire.
  • Step 4: Conclude that the electric field at a distance r from the wire is not defined by Gauss's law.
  • Gauss's Law – A principle that relates the electric flux through a closed surface to the charge enclosed by that surface.
  • Electric Field vs. Magnetic Field – Understanding the distinction between electric fields produced by static charges and magnetic fields produced by moving charges (currents).
  • Cylindrical Symmetry – The symmetry of the problem allows for simplifications in calculating electric or magnetic fields around cylindrical objects.
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