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A charged sphere has a radius R and a total charge Q. What is the electric poten

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Question: A charged sphere has a radius R and a total charge Q. What is the electric potential at a point outside the sphere at a distance r from the center (r > R)?

Options:

  1. kQ/R
  2. kQ/r
  3. kQ/(R+r)
  4. 0

Correct Answer: kQ/r

Solution: 

For a charged sphere, the electric potential outside the sphere behaves as if all the charge were concentrated at the center, so V = kQ/r.

A charged sphere has a radius R and a total charge Q. What is the electric poten

Practice Questions

Q1
A charged sphere has a radius R and a total charge Q. What is the electric potential at a point outside the sphere at a distance r from the center (r > R)?
  1. kQ/R
  2. kQ/r
  3. kQ/(R+r)
  4. 0

Questions & Step-by-Step Solutions

A charged sphere has a radius R and a total charge Q. What is the electric potential at a point outside the sphere at a distance r from the center (r > R)?
Correct Answer: V = kQ/r
  • Step 1: Understand that we have a charged sphere with a total charge Q and a radius R.
  • Step 2: Identify the point where we want to find the electric potential, which is outside the sphere at a distance r from the center (where r is greater than R).
  • Step 3: Recall that for a charged sphere, the electric potential outside the sphere can be treated as if all the charge Q is concentrated at the center of the sphere.
  • Step 4: Use the formula for electric potential V at a distance r from a point charge, which is V = kQ/r, where k is a constant (Coulomb's constant).
  • Step 5: Substitute the values into the formula to find the electric potential at the point outside the sphere.
  • Electric Potential of a Charged Sphere – The electric potential outside a uniformly charged sphere is equivalent to that of a point charge located at the center of the sphere.
  • Coulomb's Law – The relationship between electric potential and distance from a point charge, represented by the formula V = kQ/r.
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