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 linear charge density is λ C/m, then the total electric flux through all the faces of the cube is ____. (Take ε₀ as the free space permittivity)

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🔸 Concept Used

This is a classic Gauss’s Law application involving partial charge enclosure inside a cube.

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🧠 Solution:

According to Gauss’s Law:
Φ = q_enclosed / ε₀

Let’s compute the enclosed charge.

• Length of line charge = a / 2
• Linear charge density = λ
• The line lies along the center of edge BC, which is shared by 4 identical cubes.

So, only 1/4 of the line charge is enclosed within this cube:

q_enclosed = (1/4) × λ × (a / 2) = (λ a) / 8

Now apply Gauss’s Law:

Φ = q_enclosed / ε₀ = (λ a) / (8 ε₀)

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✅ Final Answer:

Φ = (λ a) / (8 ε₀)

Watch Full Video Solution JEE Mains 2025 Physics Questions (22nd Jan Shift 1)

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📌 Tip for Students:

In questions like this, always visualize how many symmetric volumes (cubes) would be needed to fully enclose the given charge.

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