A line charge of length a/2 is kept at the center of an edge BC of a cube ABCDEFGH having edge length ' a ' as shown in the figure. If the density of line charge is λ C per unit length, then the total electric flux through all the faces of the cube will be ___________. (Take, ε₀ as the free space permittivity) (a) (λ a)/(2ε₀) (b) (λ a)/(8ε₀) (c) (λ a)/(4ε₀) (d) (λ a)/(16ε₀)

Answer: (b). Charge on the edge: q = /2. A charge on an edge is shared equally by 4 cubes, so this cube gets 14 of its flux. φ = (λ a)/(2)·(1)/(4ε₀) = (λ a)/(8ε₀), answer (b).

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Electric Flux & Gauss's Law

A line charge of length $\frac{a}{2}$ is kept at the center of an edge $BC$ of a cube ABCDEFGH having edge length ' $a$ ' as shown in the figure. If the density of line charge is $\lambda\text{ C}$ per unit length, then the total electric flux through all the faces of the cube will be ___________. (Take, $\epsilon_0$ as the free space permittivity)

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Answer: (b)

Charge on the edge: $q = \lambda\frac{a}{2}$ .
A charge on an edge is shared equally by 4 cubes, so this cube gets $\frac14$ of its flux.
$\phi = \frac{\lambda a}{2}\cdot\frac{1}{4\varepsilon_0} = \frac{\lambda a}{8\varepsilon_0}$ , answer (b).

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