If a point charge Q is placed at the center of a spherical Gaussian surface of r

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Question: If a point charge Q is placed at the center of a spherical Gaussian surface of radius R, what is the electric flux through the surface?

Options:

Correct Answer: Q/ε₀

Solution:

The electric flux through a closed surface is given by Φ = Q_enc/ε₀. Here, Q_enc = Q, so Φ = Q/ε₀.

If a point charge Q is placed at the center of a spherical Gaussian surface of radius R, what is the electric flux through the surface?

If a point charge Q is placed at the center of a spherical Gaussian surface of radius R, what is the electric flux through the surface?

Correct Answer: Φ = Q/ε₀

Step 1: Understand that we have a point charge Q placed at the center of a spherical surface.
Step 2: Recall that the electric flux (Φ) through a closed surface can be calculated using Gauss's Law.
Step 3: Gauss's Law states that Φ = Q_enc / ε₀, where Q_enc is the charge enclosed by the surface and ε₀ is the permittivity of free space.
Step 4: Since the point charge Q is at the center of the spherical surface, it is completely enclosed by the surface.
Step 5: Therefore, Q_enc = Q (the charge at the center).
Step 6: Substitute Q_enc into the formula: Φ = Q / ε₀.
Step 7: This gives us the final result for the electric flux through the surface.

Gauss's Law – The relationship between electric flux through a closed surface and the charge enclosed by that surface.
Electric Flux – A measure of the quantity of electric field passing through a given area.
Spherical Symmetry – Understanding how electric fields behave in symmetric charge distributions.