A cube of side length a has a charge Q at one of its corners. What is the electric flux through one face of the cube?

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Q: A cube of side length a has a charge Q at one of its corners. What is the electric flux through one face of the cube?

Solution: The total flux through the cube is Q/ε₀, and since the charge is at one corner, the flux through one face is Q/(12ε₀).

Steps: 8

Step 1: Understand that electric flux is related to the charge enclosed by a surface.
Step 2: Recall 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 3: In this case, the cube has a charge Q located at one of its corners.
Step 4: Since the charge is at a corner, it is shared by 3 adjacent faces of the cube.
Step 5: The total flux through the entire cube is given by Φ_total = Q / ε₀.
Step 6: Since the charge is at a corner, the flux through one face of the cube is one-third of the total flux through the cube.
Step 7: However, since the charge is shared among 3 faces, we need to divide the total flux by 3, resulting in Φ_face = (Q / ε₀) / 3.
Step 8: But since the charge is at the corner, we actually consider that each face only gets 1/4 of the flux from the charge, leading to Φ_face = Q / (12ε₀).