A spherical Gaussian surface of radius R encloses a charge Q. What is the electr

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Question: A spherical Gaussian surface of radius R encloses 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 is given by E = Q/4πε₀r². At 2R, it becomes Q/4πε₀(2R)².

A spherical Gaussian surface of radius R encloses a charge Q. What is the electric field at a distance 2R from the center?

A spherical Gaussian surface of radius R encloses 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 the formula for the electric field (E) outside a spherical charge distribution: E = Q / (4πε₀r²), where r is the distance from the center.
Step 4: Substitute r with 2R in the formula: E = Q / (4πε₀(2R)²).
Step 5: Simplify the expression: E = Q / (4πε₀ * 4R²) = Q / (16πε₀R²).
Step 6: Conclude that the electric field at a distance of 2R from the center is E = Q / (16πε₀R²).

Gauss's Law – The application of Gauss's Law to determine the electric field due to a spherically symmetric charge distribution.
Electric Field Calculation – Understanding how to calculate the electric field at a distance from a point charge or spherical charge distribution.
Inverse Square Law – The principle that the electric field strength decreases with the square of the distance from the charge.