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

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Q: A point charge Q is placed at the center of a cube. What is the electric flux through one face of the cube?

Solution: The total flux through the cube is Q/ε₀. Since there are 6 faces, the flux through one face is Q/(6ε₀).

Steps: 6

Step 1: Understand that electric flux is related to the charge inside a closed surface.
Step 2: Recognize that the cube has 6 faces and the point charge Q is at the center.
Step 3: Use Gauss's Law, which states that the total electric flux (Φ) through a closed surface is equal to the charge (Q) enclosed divided by the permittivity of free space (ε₀).
Step 4: Calculate the total electric flux through the entire cube: Φ_total = Q / ε₀.
Step 5: Since the cube has 6 identical faces, the electric flux through one face is the total flux divided by 6.
Step 6: Therefore, the electric flux through one face of the cube is Φ_face = Q / (6ε₀).