If a charge of +Q is placed at one corner of a cube, what is the electric flux t

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Question: If a charge of +Q is placed at one corner of a cube, 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. Since the charge is at one corner, the flux through one face is Q/6ε₀.

If a charge of +Q is placed at one corner of a cube, what is the electric flux through one face of the cube?

If a charge of +Q is placed at one corner of a cube, what is the electric flux through one face of the cube?

Step 1: Understand that electric flux is related to the charge inside a closed surface. The total electric flux (Φ) through a closed surface is given by the formula Φ = Q/ε₀, where Q is the charge and ε₀ is the permittivity of free space.
Step 2: In this case, we have a charge of +Q placed at one corner of a cube. Since the charge is at a corner, it is shared by three adjacent faces of the cube.
Step 3: The total flux through the entire cube is Q/ε₀. However, since the charge is at a corner, we need to find out how much of that flux goes through just one face of the cube.
Step 4: The charge at the corner contributes to the flux through three faces of the cube. Therefore, the flux through one face is one-third of the total flux contributed by the charge.
Step 5: Since the total flux through the cube is Q/ε₀, the flux through one face is (1/3) * (Q/ε₀) = Q/(3ε₀).
Step 6: However, since the charge is at the corner and affects three faces, we need to divide this flux by 2 (because each face shares the flux equally), resulting in Q/(6ε₀) for one face.

Gauss's Law – The relationship between electric flux through a closed surface and the charge enclosed by that surface.
Symmetry in Electric Fields – Understanding how the placement of charges affects the distribution of electric flux through surfaces.
Flux Distribution – How to calculate the distribution of electric flux when a charge is located at a corner of a geometric shape.