What is the electric field outside a uniformly charged sphere of radius R with total charge Q?
Practice Questions
1 question
Q1
What is the electric field outside a uniformly charged sphere of radius R with total charge Q?
0
Q/(4πε₀R²)
Q/(4πε₀R)
Q/(2πε₀R²)
For a uniformly charged sphere, outside the sphere, the electric field behaves as if all the charge were concentrated at the center, E = Q/(4πε₀R²).
Questions & Step-by-step Solutions
1 item
Q
Q: What is the electric field outside a uniformly charged sphere of radius R with total charge Q?
Solution: For a uniformly charged sphere, outside the sphere, the electric field behaves as if all the charge were concentrated at the center, E = Q/(4πε₀R²).
Steps: 7
Step 1: Understand that we have a sphere with a total charge Q and radius R.
Step 2: Recognize that we are interested in the electric field outside this sphere.
Step 3: Recall that for a uniformly charged sphere, the electric field outside behaves like the field from a point charge located 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) and r is the distance from the center.
Step 5: In our case, since we are outside the sphere, we can set r = R (the radius of the sphere) for the electric field calculation.
Step 6: Substitute the values into the formula: E = (1/(4πε₀)) * Q / R².
Step 7: Conclude that the electric field outside the uniformly charged sphere is E = Q/(4πε₀R²).
