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If the radius of a spherical Gaussian surface is doubled while keeping the charg

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Question: If the radius of a spherical Gaussian surface is doubled while keeping the charge inside constant, how does the electric field change?

Options:

  1. It doubles
  2. It halves
  3. It remains the same
  4. It quadruples

Correct Answer: It halves

Solution: 

The electric field E due to a point charge decreases with the square of the distance from the charge, so if the radius is doubled, the electric field halves.

If the radius of a spherical Gaussian surface is doubled while keeping the charg

Practice Questions

Q1
If the radius of a spherical Gaussian surface is doubled while keeping the charge inside constant, how does the electric field change?
  1. It doubles
  2. It halves
  3. It remains the same
  4. It quadruples

Questions & Step-by-Step Solutions

If the radius of a spherical Gaussian surface is doubled while keeping the charge inside constant, how does the electric field change?
Correct Answer: Electric field halves.
  • Step 1: Understand that we have a spherical Gaussian surface around a point charge.
  • Step 2: Recall that the electric field (E) created by a point charge decreases with distance from the charge.
  • Step 3: Remember the formula for the electric field due to a point charge: E = k * Q / r^2, where k is a constant, Q is the charge, and r is the distance from the charge.
  • Step 4: Note that if we double the radius (r) of the spherical surface, we are increasing the distance from the charge.
  • Step 5: Since the radius is doubled, we replace r with 2r in the formula: E = k * Q / (2r)^2.
  • Step 6: Simplify the equation: E = k * Q / (4r^2). This shows that the electric field is now one-fourth of what it was at the original radius.
  • Step 7: Since the electric field is inversely proportional to the square of the distance, doubling the radius results in the electric field being halved.
  • Electric Field and Gauss's Law – Understanding how the electric field behaves in relation to distance from a point charge, particularly how it decreases with the square of the distance.
  • Spherical Gaussian Surface – Application of Gauss's Law to a spherical surface and how it relates to the charge enclosed.
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