The figure shows a Gaussian surface in the shape of a cube w

The figure shows a Gaussian surface in the shape of a cube with edge length 1.60 m. What are the net flux through the surface and the net charge q_enc enclosed by the surface if the electric field in the region is in the positive y direction and has a magnitude that is given by E = 2.34y N/C? What are the net flux and net enclosed charge if the electric field is in the xy plane and has components E_x = -4.85 N/C and E_y = (8.37 + 2.34y) N/C?

Solution

a ) for left face,

E = 2.34 x (-1.60/2) = -1.872 N/C j

A = - 1.60^2 j = -2.56 j

flux = E.A = 4.79 Wb

for right face

E = 2.34 x (1.60/2) = 1.872 N/C j

A = 1.60^2 j = 2.56 j

flux = E.A = 4.79 Wb

total flux = 4.79 + 4.79 = 9.58 Wb

b) flux = qin/e0 (from Guass law)

9.58 = qin / (8.858 x 10^-12)

qin = 8.49 x 10^-11 C

c) Ex is same from both surface so flux will get cancel.

Ey = 8.37 + 2.34y

same with 8.37 terms .

so there will be only effecr of 2.34y.

hence, total flux = 9.58 Wb

d) qin = 8.49 x 10^-11 C