What is the electric field at a distance r from a uniformly charged sphere of ra

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Question: What is the electric field at a distance r from a uniformly charged sphere of radius R and total charge Q, when r > R?

Options:

Correct Answer: Q/(4πε₀r²)

Solution:

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

What is the electric field at a distance r from a uniformly charged sphere of radius R and total charge Q, when r > R?

What is the electric field at a distance r from a uniformly charged sphere of radius R and total charge Q, when r > R?

Step 1: Understand that we have a uniformly charged sphere with a total charge Q and radius R.
Step 2: Identify the distance r from the center of the sphere, where r is greater than R (r > R).
Step 3: Recall that for points outside a uniformly charged sphere, the electric field behaves 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 is Coulomb's constant (1/(4πε₀)).
Step 5: Substitute k with 1/(4πε₀) in the formula, so we have E = (1/(4πε₀)) * Q / r².
Step 6: Simplify the expression to get the final formula for the electric field: E = Q / (4πε₀r²).

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