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