In a cuboid of dimension 2L × 2L × L, a charge q is placed at the center of the surface ' S ' having area of 4L². The flux through the opposite surface to ' S ' is given by (a) (q)/(2ε₀) (b) (q)/(3ε₀) (c) (q)/(12ε₀) (d) (q)/(6ε₀)

Answer: (d). Put an identical cuboid on the other side of S: together they form a cube of side 2L with q at its centre. Each face of that cube gets (q)/(6ε₀). The face opposite S is one such face, so φ = (q)/(6ε₀), answer (d).

In a cuboid of dimension 2L × 2L × L, a charge q is placed at the… | JEE Main 2023 (29 Jan, Shift 1)

Q67JEE Main 2023 · 29 JAN · SHIFT 1Medium

Electric Flux & Gauss's Law

In a cuboid of dimension $2L \times 2L \times L$ , a charge $q$ is placed at the center of the surface ' $S$ ' having area of $4L^{2}$ . The flux through the opposite surface to ' $S$ ' is given by

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Answer: (d)

Put an identical cuboid on the other side of S: together they form a cube of side $2L$ with $q$ at its centre.
Each face of that cube gets $\frac{q}{6\varepsilon_0}$ .
The face opposite S is one such face, so $\phi = \frac{q}{6\varepsilon_0}$ , answer (d).

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