Question

Law of Gauss

1. Consider a constant vector field of the form v = (1, 1, 1)N/C and a closed area with cubic shape of side 1m oriented as desired.
a) What is the flow of v through the cube?
b) If now a point load of 1C is introduced into the cubic surface. What will be the total electric field flow through the cube?
(Note step by step)

Answer 1

a) Since the vector field is constant, the field lines entering into the cube, will leave the cube as well. So, net flux flow through the cube is zero.

b) According to Gauss law, flux flow through a closed surface is given by: f=q/$\epsilon$₀ where f is flux flow through the cube, q is charge inside the closed surface, $\epsilon$ ₀ is permittivity of free space with value 8.85*10^-12 C²/(N-m²).

Here, q=1C, So, f= 1/(8.85*10^-12)= 1.13 *10¹¹ V-m.