A uniformly charged sphere of radius R has a total charge Q. What is the electric field at a point outside the sphere (r > R)?
Practice Questions
1 question
Q1
A uniformly charged sphere of radius R has a total charge Q. What is the electric field at a point outside the sphere (r > R)?
0
Q/(4πε₀r²)
Q/(4πε₀R²)
Q/(4πε₀R)
For a uniformly charged sphere, the electric field outside the sphere behaves as if all the charge were concentrated at the center, thus E = Q/(4πε₀r²).
Questions & Step-by-step Solutions
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Q
Q: A uniformly charged sphere of radius R has a total charge Q. What is the electric field at a point outside the sphere (r > R)?
Solution: For a uniformly charged sphere, the electric field outside the sphere behaves as if all the charge were concentrated at the center, thus E = Q/(4πε₀r²).
Steps: 6
Step 1: Understand that we have a sphere with a total charge Q and radius R.
Step 2: Identify the point where we want to find the electric field, which is outside the sphere (r > R).
Step 3: Recall that for a uniformly charged sphere, the electric field outside the sphere acts as if all the charge is 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 = 1/(4πε₀).
Step 5: Substitute k into the formula to get E = Q / (4πε₀r²).
Step 6: Conclude that the electric field at a point outside the sphere is given by E = Q / (4πε₀r²).
