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

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

Solution: The total electric flux through the Gaussian surface is given by Φ = Q/ε₀, where Q is the charge enclosed.

Steps: 6

Step 1: Understand that a point charge Q is placed at the center of a spherical surface.
Step 2: Recall that electric flux (Φ) through a surface is related to the charge enclosed by that surface.
Step 3: Use Gauss's Law, which states that the total electric flux Φ through a closed surface is equal to the charge enclosed (Q) divided by the permittivity of free space (ε₀).
Step 4: Write the formula for electric flux: Φ = Q / ε₀.
Step 5: Since the charge Q is at the center of the spherical surface, it is completely enclosed by the surface.
Step 6: Conclude that the total electric flux through the spherical Gaussian surface is Φ = Q / ε₀.