A cube encloses a charge Q at its center. What is the electric flux through one

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Question: A cube encloses a charge Q at its center. What is the electric flux through one face of the cube?

Options:

Correct Answer: Q/6ε₀

Solution:

The total flux through the cube is Q/ε₀, and since there are 6 faces, the flux through one face is Q/6ε₀.

A cube encloses a charge Q at its center. What is the electric flux through one face of the cube?

A cube encloses a charge Q at its center. What is the electric flux through one face of the cube?

Step 1: Understand that a cube has 6 faces and encloses a charge Q at its center.
Step 2: Recall 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 3: Apply Gauss's Law to the cube: The total electric flux through the entire cube is Φ = Q/ε₀.
Step 4: Since the cube has 6 identical faces, the electric flux is evenly distributed across all faces.
Step 5: To find the electric flux through one face, divide the total flux by the number of faces: Φ_face = (Q/ε₀) / 6.
Step 6: Simplify the expression: Φ_face = Q / (6ε₀).

Gauss's Law – The total electric flux through a closed surface is proportional to the charge enclosed within that surface.
Symmetry in Electric Fields – For symmetrical charge distributions, the electric flux can be evenly distributed across all faces of the enclosing surface.