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A point charge of +Q is placed at the center of a spherical shell of radius R wi

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Question: A point charge of +Q is placed at the center of a spherical shell of radius R with surface charge density σ. What is the electric field inside the shell?

Options:

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

Correct Answer: 0

Solution: 

According to Gauss\'s law, the electric field inside a conductor in electrostatic equilibrium is zero.

A point charge of +Q is placed at the center of a spherical shell of radius R wi

Practice Questions

Q1
A point charge of +Q is placed at the center of a spherical shell of radius R with surface charge density σ. What is the electric field inside the shell?
  1. 0
  2. Q/(4πε₀R²)
  3. σ/ε₀
  4. Q/(4πε₀R)

Questions & Step-by-Step Solutions

A point charge of +Q is placed at the center of a spherical shell of radius R with surface charge density σ. What is the electric field inside the shell?
  • Step 1: Understand that we have a point charge of +Q at the center of a spherical shell.
  • Step 2: Recognize that the spherical shell has a surface charge density σ, which means it has charge distributed over its surface.
  • Step 3: Recall Gauss's law, which states that the electric field inside a closed conductor in electrostatic equilibrium is zero.
  • Step 4: Since the spherical shell is a conductor and is in electrostatic equilibrium, the electric field inside the shell must be zero.
  • Step 5: Conclude that regardless of the charge +Q at the center, the electric field inside the shell remains zero.
  • Gauss's Law – A principle that relates the electric field to the charge enclosed by a closed surface.
  • Electric Field in Conductors – In electrostatic equilibrium, the electric field inside a conductor is zero.
  • Surface Charge Density – The amount of charge per unit area on the surface of the spherical shell.
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