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

Solution: The charge at one corner contributes 1/8 of its flux to the cube. Thus, total flux = (1/8)Q/ε₀ = Q/(12ε₀).

Steps: 8

Step 1: Understand that a cube has 8 corners.
Step 2: Recognize that a charge at one corner of the cube affects the electric flux through the cube.
Step 3: Realize that the total electric flux from a point charge Q is given by the formula Φ = Q/ε₀, where ε₀ is the permittivity of free space.
Step 4: Since the charge is at a corner, only 1/8 of the total flux from the charge will pass through the cube.
Step 5: Calculate the flux contributed by the charge to the cube: (1/8) * (Q/ε₀).
Step 6: Simplify the expression: (1/8) * (Q/ε₀) = Q/(8ε₀).
Step 7: Since the cube has 6 faces, the total flux through the cube is Q/(8ε₀) multiplied by 1 (as it only contributes to one face).
Step 8: The final total electric flux through the cube is Q/(12ε₀).