Consider a uniform electric field E = 3 × 10³î N/C. (a) What is the flux of this field through a square of 10 cm on a side whose plane is parallel to the yz plane? (b) What is the flux through the same square if the normal to its plane makes a 60° angle with the x-axis?

Given:

Electric field E = 3 × 10³ N/C

Side of square, s = 10 cm

a) Flux of field through square whose plane is parallel to yz plane.

We understand that the normal to the plane is parallel to the direction of field.

So, θ = 0°

Φ = E . A

Φ = E × A × cos(θ) …(1)

Where, E = Electric field

A = Area through which we have to calculate flux

θ = Angle between normal to surface and the Electric field

A = s²

A = .01 m²

Plugging values, of E, A and θ in equation (1)

Φ = 3 × 10³ NC^-1 × 0.01m² × cos0°

Φ = 30 Nm²C^-1

b) If normal to its (square’s) plane makes 60° with the X axis.

θ = 60°

Φ = E × A × cos(θ)

Φ = 3 × 10³ NC^-1 × 0.01m² × cos60°

Φ = 15 Nm²C^-1