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If a charge Q is uniformly distributed over a spherical surface of radius R, wha

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Question: If 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 a distance r from the center (r > R)?

Options:

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

Correct Answer: Q/(4πε₀r²)

Solution: 

For a point outside the sphere, the electric field behaves as if all the charge were concentrated at the center, hence E = Q/(4πε₀r²).

If a charge Q is uniformly distributed over a spherical surface of radius R, wha

Practice Questions

Q1
If 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 a distance r from the center (r > R)?
  1. 0
  2. Q/(4πε₀r²)
  3. Q/(4πε₀R²)
  4. Q/(4πε₀R)

Questions & Step-by-Step Solutions

If 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 a distance r from the center (r > R)?
  • Step 1: Understand that we have a spherical surface with a charge Q distributed evenly over it.
  • Step 2: Identify the radius of the sphere, which is R.
  • Step 3: Recognize that we are looking for the electric field at a point outside the sphere, at a distance r from the center, where r is greater than R (r > R).
  • Step 4: 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 5: Use the formula for the electric field due to a point charge, which is E = Q/(4πε₀r²), where ε₀ is the permittivity of free space.
  • Step 6: Substitute the charge Q and the distance r into the formula to find the electric field at that point.
  • 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 due to a symmetric charge distribution can be treated as if all the charge were concentrated at a point.
  • Electric Field of a Sphere – For a uniformly charged sphere, the electric field at a point outside the sphere is inversely proportional to the square of the distance from the center.
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