Question

A plane surface, in shape of a square of side 1 cm is placed in an electric field `vecE = (100 N/C)hati` such that the unit vector normal to the surface is

given by `hatn = 0.8hati + 0.6hatk`. Find the electric flux through the surface.

Answer 1

`vecE = (100 N/C)hati`

Side = 1 cm = 0.01 m

Surface area, A = (0.01)² = 1 × 10⁻⁴ m²

Normal unit vector,

`hatn = 0.8 hati + 0.6 hatk`

Angle, `theta = tan^-1(0.6/0.8) = 36.87^circ`

Now, Φ = EA cos θ

Φ = 100(1 × 10⁻⁴) cos 36.87

Φ = 10⁻² × 0.8

Φ = 8 × 10⁻³ Nm²/C