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A charge Q is uniformly distributed over a spherical surface of radius R. What i

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Question: A charge Q is uniformly distributed over a spherical surface of radius R. What is the electric field at a point outside the sphere at distance r from the center?

Options:

  1. 0
  2. Q/4πε₀r²
  3. Q/4πε₀R²
  4. Q/4πε₀R

Correct Answer: Q/4πε₀r²

Solution: 

For points outside the sphere, the electric field behaves as if all the charge were concentrated at the center, so E = Q/4πε₀r².

A charge Q is uniformly distributed over a spherical surface of radius R. What i

Practice Questions

Q1
A charge Q is uniformly distributed over a spherical surface of radius R. What is the electric field at a point outside the sphere at distance r from the center?
  1. 0
  2. Q/4πε₀r²
  3. Q/4πε₀R²
  4. Q/4πε₀R

Questions & Step-by-Step Solutions

A charge Q is uniformly distributed over a spherical surface of radius R. What is the electric field at a point outside the sphere at distance r from the center?
  • Step 1: Understand that we have a spherical surface with a total charge Q distributed evenly over it.
  • Step 2: Identify the point where we want to find the electric field. This point is outside the sphere at a distance r from the center.
  • Step 3: Recall that for points outside a uniformly charged sphere, the electric field behaves as if all the charge were concentrated at the center of the sphere.
  • Step 4: Use the formula for the electric field due to a point charge, which is E = k * Q / r², where k is the constant 1/(4πε₀).
  • Step 5: Substitute k with 1/(4πε₀) in the formula to get E = Q / (4πε₀r²).
  • Step 6: Conclude that the electric field at the point outside the sphere is E = Q / (4πε₀r²).
  • Gauss's Law – The electric field outside a uniformly charged spherical surface can be determined using Gauss's Law, which states that the electric field behaves as if the charge were concentrated at a point at the center.
  • Electric Field of a Sphere – For a uniformly charged sphere, the electric field outside the sphere is inversely proportional to the square of the distance from the center.
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