For a spherical Gaussian surface of radius R enclosing a charge Q, what is the e

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Question: For a spherical Gaussian surface of radius R enclosing a charge Q, what is the electric field at a distance 2R from the center?

Options:

Correct Answer: Q/4πε₀(2R)²

Solution:

The electric field outside a spherical charge distribution behaves as if all the charge were concentrated at the center, so E = Q/4πε₀r².

For a spherical Gaussian surface of radius R enclosing a charge Q, what is the electric field at a distance 2R from the center?

For a spherical Gaussian surface of radius R enclosing a charge Q, what is the electric field at a distance 2R from the center?

Step 1: Understand that we have a spherical Gaussian surface with a radius R that encloses a charge Q.
Step 2: Recognize that we want to find the electric field at a distance of 2R from the center of the sphere.
Step 3: Recall that for a spherical charge distribution, the electric field outside the sphere behaves as if all the charge is concentrated at the center.
Step 4: Use the formula for the electric field due to a point charge: E = Q / (4πε₀r²), where r is the distance from the center.
Step 5: Substitute r = 2R into the formula: E = Q / (4πε₀(2R)²).
Step 6: Simplify the expression: E = Q / (4πε₀ * 4R²) = Q / (16πε₀R²).

Gauss's Law – Understanding how to apply Gauss's Law to determine the electric field due to a spherically symmetric charge distribution.
Electric Field of Point Charges – Recognizing that the electric field outside a spherical charge distribution can be treated as if all the charge is concentrated at a point at the center.