A square sheet of 5.0 cm is placed in an electric field E = (1.6 × 10⁴ \(\frac{N}{C}\)) i such that the normal unit vector for the sheet is [(\(\frac{\sqrt3}{2}\))i + \((\frac{1}{2})\)j]. The electric flux through the sheet is:

Question

Question

This question was previously asked in

AAI ATC Junior Executive 27 July 2022 Shift 1 Official Paper

Answer 1

=Concept:

Electric flux: It is defined as the total number of electric field lines passing a given area in a unit of time.

Formula, electric flux, ϕE = EA cosθ, where, E = electric field, A = surface area, θ = angle between the electric field and the area vector

Calculation:

Given,

The electric field, E = (1.6 × 104 \(\frac{N}{C}\)) i

Side of the square sheet, a = 5.0 cm = 0.05 m

Surface area, s = a² = (0.05)² = 2.5 × 10^-3 m²

The normal unit vector, r = [(\(\frac{\sqrt3}{2}\))i + \((\frac{1}{2})\)j].

Angle, \(θ=\tan^{-1} (\frac{1/2}{\sqrt{3}/2}) \)

θ = 30º

The formula for the electric flux, ϕ_E = EA cosθ

ϕE = 1.6 × 10⁴ × 2.5 × 10-3 × cos 30º

ϕE = 34.6 Nm²/C

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