An electric field, E = (2i + 6j + 8k)/(√(6)) passes through the surface of 4 m² area having unit vector n = ((2i + j + k)/(√(6))). The electric flux for that surface is _________ V m. Numerical answer type. Work it out, then open the answer.

Answer: 12. φ = ( E· n)A E· n = (2(2) + 6(1) + 8(1))/(√6·√6) = 18/6 = 3 V/m φ = 3×4 = 12 V m

An electric field, E = (2i + 6j + 8k)/(√(6)) passes through the… | JEE Main 2024 (8 Apr, Shift 1)

Q36JEE Main 2024 · 8 APR · SHIFT 1Easy

Electric Flux & Gauss's Law

An electric field, $\vec{E} = \frac{2\hat{i} + 6\hat{j} + 8\hat{k}}{\sqrt{6}}$ passes through the surface of $4\text{ m}^2$ area having unit vector $\hat{n} = \left(\frac{2\hat{i} + \hat{j} + \hat{k}}{\sqrt{6}}\right)$ . The electric flux for that surface is _________ $\text{V m}$ .

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

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Answer: 12

$\phi = (\vec E\cdot\hat n)A$
$\vec E\cdot\hat n = \dfrac{2(2) + 6(1) + 8(1)}{\sqrt6\cdot\sqrt6} = \dfrac{18}{6} = 3$ V/m
$\phi = 3\times4 = 12$ V m

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