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A point charge +Q is placed at the center of a spherical Gaussian surface of rad

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Question: A point charge +Q is placed at the center of a spherical Gaussian surface of radius R. What is the electric flux through the surface?

Options:

  1. 0
  2. Q/ε₀
  3. Q/(4πε₀R²)
  4. Q/(4πε₀R)

Correct Answer: Q/ε₀

Solution: 

The electric flux through the Gaussian surface is given by Φ = Q/ε₀, where Q is the charge enclosed.

A point charge +Q is placed at the center of a spherical Gaussian surface of rad

Practice Questions

Q1
A point charge +Q is placed at the center of a spherical Gaussian surface of radius R. What is the electric flux through the surface?
  1. 0
  2. Q/ε₀
  3. Q/(4πε₀R²)
  4. Q/(4πε₀R)

Questions & Step-by-Step Solutions

A point charge +Q is placed at the center of a spherical Gaussian surface of radius R. What is the electric flux through the surface?
  • Step 1: Identify the charge enclosed by the Gaussian surface. In this case, it is +Q.
  • Step 2: Recall the formula for electric flux (Φ) through a closed surface, which is Φ = Q/ε₀, where ε₀ is the permittivity of free space.
  • Step 3: Substitute the value of the enclosed charge (Q) into the formula: Φ = +Q/ε₀.
  • Step 4: Conclude that the electric flux through the spherical Gaussian surface is Φ = +Q/ε₀.
  • 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, integrated over the surface.
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