If a charge Q is uniformly distributed over a sphere of radius R, what is the electric field at a distance r from the center where r > R?

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Q: If a charge Q is uniformly distributed over a sphere of radius R, what is the electric field at a distance r from the center where r > R?

Solution: For r > R, the electric field behaves as if all the charge were concentrated at the center, given by E = Q/(4πε₀r²).

Steps: 6

Step 1: Understand that we have a sphere with a total charge Q distributed evenly over its surface.
Step 2: Identify the radius of the sphere, which is R.
Step 3: Recognize that we are interested in finding the electric field at a point that is outside the sphere, specifically at a distance r from the center, where r is greater than 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 total charge Q and the distance r into the formula to find the electric field at that point.