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A uniform electric field E = E0 x̂ (E0 constant) fills a region. A square plate of side 'a' is oriented so that it lies along a face diagonal of a cube, i.e. its plane is tilted at 45 deg to the x-axis so that the plate's area vector makes a 45 deg angle with the field. What is the electric flux through this square plate?

1. E0*a²
2. 2*E0*a²
3. sqrt(2)*E0*a²
4. E0*a²/sqrt(2)

Correct answer: E0*a²

Solution

Only the component of the field perpendicular to the plate contributes to flux. The diagonal plate has a larger area than a face (a * a*sqrt(2)) but its normal is inclined at 45 deg, and the two factors combine to give the same flux as a unit face perpendicular to the field.

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