A point charge +Q is placed at the center of a spherical Gaussian surface. What

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Question: A point charge +Q is placed at the center of a spherical Gaussian surface. What is the total electric flux through the surface?

Options:

Correct Answer: 4πQ/ε₀

Solution:

The total electric flux through the surface is given by Gauss\'s law as Φ = Q/ε₀, and for a point charge at the center, it results in 4πQ/ε₀.

A point charge +Q is placed at the center of a spherical Gaussian surface. What is the total electric flux through the surface?

A point charge +Q is placed at the center of a spherical Gaussian surface. What is the total electric flux through the surface?

Step 1: Understand what a point charge is. A point charge is a charged object that has a very small size compared to the distance from it.
Step 2: Know what a spherical Gaussian surface is. It is an imaginary sphere used to help calculate electric fields and flux.
Step 3: Recall Gauss's law. It states that the total electric flux (Φ) through a closed surface is equal to the charge (Q) inside the surface divided by the permittivity of free space (ε₀).
Step 4: Identify the charge inside the Gaussian surface. In this case, it is the point charge +Q placed at the center.
Step 5: Apply Gauss's law. Since the charge +Q is at the center, the total electric flux through the surface is Φ = Q/ε₀.
Step 6: Calculate the total electric flux. For a point charge, the total electric flux can also be expressed as Φ = 4πQ/ε₀, which accounts for the spherical symmetry.

Gauss's Law – Gauss's law relates the electric flux through a closed surface to the charge enclosed by that surface, stating that the total electric flux Φ is equal to the enclosed charge Q divided by the permittivity of free space ε₀.
Spherical Symmetry – The problem utilizes the symmetry of a spherical Gaussian surface, which simplifies the calculation of electric flux due to a point charge at its center.