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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 point outside the cylinder?

Options:

  1. Zero
  2. Directly proportional to the distance from the wire
  3. Inversely proportional to the distance from the wire
  4. Constant

Correct Answer: Directly proportional to the distance from the wire

Solution: 

The electric field outside the cylindrical surface is directly proportional to the distance from the wire.

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 point outside the cylinder?
  1. Zero
  2. Directly proportional to the distance from the wire
  3. Inversely proportional to the distance from the wire
  4. Constant

Questions & Step-by-Step Solutions

A cylindrical Gaussian surface encloses a long straight wire carrying a current. What is the electric field at a point outside the cylinder?
  • Step 1: Understand that we have a long straight wire carrying an electric current.
  • Step 2: Recognize that the wire creates an electric field around it.
  • Step 3: Identify that we are looking at a cylindrical Gaussian surface that surrounds the wire.
  • Step 4: Note that the electric field is strongest near the wire and decreases as you move away from it.
  • Step 5: Realize that the electric field at a point outside the cylinder depends on the distance from the wire.
  • Step 6: Conclude that the electric field outside the cylindrical surface is directly proportional to the distance from the wire.
  • Gauss's Law – The relationship between electric field and charge distribution, particularly for symmetric charge configurations.
  • Electric Field of a Long Straight Wire – The electric field produced by a long straight wire is inversely proportional to the distance from the wire.
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