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

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

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

Correct Answer: Q/(12ε₀)

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).

Gauss's Law – The total electric flux through a closed surface is proportional to the charge enclosed within that surface.
Symmetry in Charge Distribution – Understanding how a charge located at a corner of a cube affects the flux through the entire cube.
Fraction of Flux Contribution – Recognizing that a charge at a corner contributes only a fraction of its total flux to the cube.