A charge q is located at the centre of a cube. The electric flux through any face is:
- \(\frac {2\pi q}{6(4πε_0)}\)
- \(\frac {4\pi q}{6(4πε_0)}\)
- \(\frac {\pi q}{6(4πε_0)}\)
- \(\frac {q}{6(4πε_0)}\)
The Correct Option is B
Solution and Explanation
Total flux passing through the close cube \(ϕ = \frac {q}{ε_0}\)
All six surfaces exhibit symmetry with respect to the charge, resulting in an equal contribution to the flux. Consequently, the flux through any single face is:
\(ϕ = \frac ϕ 6 = \frac {q}{6ε_0}\)
\(φ_{face} = \frac {q}{6ε_0} = \frac {4\pi q}{6(4\piε_0)}\)
So, the correct option is (B): \(\frac {4\pi q}{6(4πε_0)}\)
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Concepts Used:
Gauss Law
Gauss law states that the total amount of electric flux passing through any closed surface is directly proportional to the enclosed electric charge.
Gauss Law:
According to the Gauss law, the total flux linked with a closed surface is 1/ε0 times the charge enclosed by the closed surface.
For example, a point charge q is placed inside a cube of edge ‘a’. Now as per Gauss law, the flux through each face of the cube is q/6ε0.
Gauss Law Formula:
As per the Gauss theorem, the total charge enclosed in a closed surface is proportional to the total flux enclosed by the surface. Therefore, if ϕ is total flux and ϵ0 is electric constant, the total electric charge Q enclosed by the surface is;
Q = ϕ ϵ0
The Gauss law formula is expressed by;
ϕ = Q/ϵ0
Where,
Q = total charge within the given surface,
ε0 = the electric constant.