A square surface of side L meter in the plane of the paper is placed in a uniform electric field E (volt/m) acting along the same plane at an angle θ with the horizontal side of the square as shown in figurre. The electric flux linked to the surface, in units of volt m is (a) (b) EL2cos θ (c) EL2sin θ (d) zero EL2

Answer: (d). φ = EAcos α, where α is the angle between E and the normal to the surface. E lies in the plane of the square, so it is perpendicular to the normal: α = 90°. φ = EL²cos 90° = 0; the angle θ does not matter. So the answer is (d) zero.

A square surface of side L meter in the plane of the paper is placed… | NEET 2010 (AIPMT, Prelims)

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Electric Flux & Gauss's Law

A square surface of side L meter in the plane of the paper is placed in a uniform electric field $E$ (volt/m) acting along the same plane at an angle $\theta$ with the horizontal side of the square as shown in figurre.

The electric flux linked to the surface, in units of volt m is

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Answer: (d)

$\phi = EA\cos\alpha$ , where $\alpha$ is the angle between $\vec E$ and the normal to the surface.
$\vec E$ lies in the plane of the square, so it is perpendicular to the normal: $\alpha = 90^\circ$ .
$\phi = EL^2\cos90^\circ = 0$ ; the angle $\theta$ does not matter.
So the answer is (d) zero.

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