Given a uniform electric field E = 5 x 10^3 i N/C, find the flux of this field through a square of 10 cm

Question

Given a uniform electric field E = 5 x 10³\(\hat i\) N/C, find the flux of this field through a square of 10 cm on a side whose plane is parallel to the Y-Z plane. What would be the flux through the same square if the plane makes a 30° angle with the X-axis? 

Answer 1

Here, \(\vec E\) = 5 x 10³\(\hat i\) N/C, i.e., field is along positive direction of X - axis.

Surface area, A  = 10 cm x 10 cm = 0.10 m x 0.10 m = 10^-2m²

(i) When plane is parallel to Y-Z plane, the normal to plane is along X - axis. Here

θ = 0°

(ii) When the plane makes a 30° angle with the X-axis, the normal to its plane makes 60° angle with X - axis.

Hence θ = 60°