Question

Figure above shows a closed Gaussian surface in the shape of a cube of edge length
3.Om. There exists an electric field given by Ē = [(2.0x + 4.0)i + 8.0j + 3.0 k] NC, where
x is in metres, in the region in which it lies. The net charge in coulombs enclosed by the
cube is equal to
(A)-54 €0
(B) 6 eo
(C) 5 50
(D) 54 eo
RX​

Answer 1

answer :

explanation : see figure for better understanding.

first of all, find electric flux through the cube.

flux through the cube , $\Phi$ = E.A

flux through the cube along x - axis = $E_x.A_x$

= (2 × 0 + 4)i . (3)² i + (2 × -3 + 4)i. (-3)²i

= 36 + 18 = 54

electric flux through the cube along y-axis = $E_yA_y$

= (8)j . (3)² j + (8)j.(-3)² j

= 72 -72 = 0

electric flux through the cube along z-axis

= (3)k. (3)² k+ (3)k.(-3)k

= 27 - 27 = 0

hence, net electric flux through the cube = 54 + 0 + 0 = 54

now from Gauss theorem,

$\frac{q_{in}}{\epsilon_0}$ = 54

so, $q_{in}=54\epsilon_0$

hence, option (D) is correct choice.