An electric charge q is placed at one of the corner points of a cube of side a. What will bethe net outwards flux coming out of the cube due to the point charge?
Question
An electric charge q is placed at one of the corner points of a cube of side a. What will bethe net outwards flux coming out of the cube due to the point charge?
Solution
The net outward flux Φ through any closed surface surrounding a charge q is given by Gauss's Law, which states:
Φ = q/ε₀
where ε₀ is the permittivity of free space.
In this case, the charge q is placed at one of the corners of the cube. However, the cube is just part of the total closed surface surrounding the charge. In fact, if we imagine a larger cube that has the original cube at one of its corners, the charge would be at the center of this larger cube.
Since the flux is evenly distributed throughout the larger cube, and our original cube is 1/8th of the larger cube (since it's at the corner), the flux through the original cube is 1/8th of the total flux.
So, the net outward flux Φ' coming out of the cube due to the point charge is:
Φ' = Φ/8 = q/(8ε₀)
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