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)?
Practice Questions
1 question
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)?
0
Q/(4πε₀r²)
Q/(4πε₀R²)
Q/(4πε₀R)
For a point outside the sphere, the electric field behaves as if all the charge were concentrated at the center, hence E = Q/(4πε₀r²).
Questions & Step-by-step Solutions
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Q
Q: 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)?
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).
Steps: 6
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.
