For a uniformly charged sphere of radius R and total charge Q, what is the elect

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Question: For a uniformly charged sphere of radius R and total charge Q, what is the electric field at a distance r from the center where 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, given by E = Q/(4πε₀r²).

For a uniformly charged sphere of radius R and total charge Q, what is the electric field at a distance r from the center where r > R?

For a uniformly charged sphere of radius R and total charge Q, what is the electric field at a distance r from the center where r > R?

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 at a distance r from the center of the sphere, and note that 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 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 Coulomb's 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 a distance r from the center of the sphere, where r > R, is given by E = Q / (4πε₀r²).

Gauss's Law – The electric field outside a uniformly charged sphere can be determined using Gauss's Law, which states that the electric field due to a symmetric charge distribution behaves as if all the charge were concentrated at a point at the center.
Electric Field Calculation – Understanding how to calculate the electric field at a distance greater than the radius of a charged object, applying the formula E = Q/(4πε₀r²).