A charge q is placed at the center of one of the surfaces of a cube. The flux linked with the cube is

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Solution

Q.
A charge q is placed at the center of one of the surfaces of a cube. The flux linked with the cube is [2024]

1 $\frac{q}{2 ε_{0}}$

2 $\frac{q}{4 ε_{0}}$

3 $\frac{q}{8 ε_{0}}$

4 $zero$

Ans.
(1)

$ϕ_{total} = \frac{q_{en}}{ε_{0}}$

Let us enclose the charge with an identical cube as shown,

$Total flux, 2 ϕ = \frac{q}{ε_{0}} \Rightarrow ϕ = \frac{q}{2 ε_{0}}$

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