As shown in figure, a cuboid lies in a region with electric field E = 2x²i - 4yj + 6k N/C. The magnitude of charge within the cuboid is nε₀ C. The value of n is _________ (if dimension of cuboid is 1 × 2 × 3 m³) Numerical answer type. Work it out, then open the answer.

Answer: 12. Cuboid: 0≤ x≤1, 0≤ y≤2, 0≤ z≤3. x = 1 face: 2(1)²×(2×3) = 12; x = 0 face: 0. y = 2 face: -4(2)×(1×3) = -24; y = 0 face: 0. The constant Ez gives zero net flux. φ = 12 - 24 = -12, so |q| = 12ε₀ and n = 12.

As shown in figure, a cuboid lies in a region with electric field E =… | JEE Main 2023 (30 Jan, Shift 2)

Q68JEE Main 2023 · 30 JAN · SHIFT 2Medium

Electric Flux & Gauss's Law

As shown in figure, a cuboid lies in a region with electric field $E = 2x^{2}\hat{i} - 4y\hat{j} + 6\hat{k}\text{ N/C}$ . The magnitude of charge within the cuboid is $n\epsilon_0\text{ C}$ .

The value of $n$ is _________ (if dimension of cuboid is $1 \times 2 \times 3\text{ m}^{3}$ )

Numerical answer type. Work it out, then open the answer.

Show answer and solution

Answer: 12

Cuboid: $0\le x\le1$ , $0\le y\le2$ , $0\le z\le3$ .
$x = 1$ face: $2(1)^2\times(2\times3) = 12$ ; $x = 0$ face: 0.
$y = 2$ face: $-4(2)\times(1\times3) = -24$ ; $y = 0$ face: 0. The constant $E_z$ gives zero net flux.
$\phi = 12 - 24 = -12$ , so $|q| = 12\varepsilon_0$ and $n = 12$ .

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Electric Flux & Gauss's Law question from JEE Main 2023 (30 Jan, Shift 2)

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