The figure shows a Gaussian surface in the shape of a cube with edge length 1.17

Question

The figure shows a Gaussian surface in the shape of a cube with edge length 1.17 m. What are (a) the net flux through the surface and (b) the net charge (in C) 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 = 3.35y N/C? What are (c) the net flux and (d) net enclosed charge (in C) if the electric field is in the xy plane and has components Ex = -5.97 N/C and Ey = (4.76 + 2.44y) N/C?
http://edugen.wileyplus.com/edugen/courses/crs4957/art/qb/EAT_1292341756226_0_7211808876146629.gif
http://edugen.wileyplus.com/edugen/courses/crs4957/art/qb/EAT_1292341756226_0_7211808876146629.gif
The figure shows a Gaussian surface in the shape of a cube with edge length 1.17 m. What are (a) the net flux through the surface and (b) the net charge (in C) 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 = 3.35y N/C? What are (c) the net flux and (d) net enclosed charge (in C) if the electric field is in the xy plane and has components Ex = -5.97 N/C and Ey = (4.76 + 2.44y) N/C?

Explanation / Answer

the net flux through the surface is

O = E x A

where E = 3.35y N/C and A = a^2,a is side of cube

Also,

O = (q_enclosed/e_o)

or q_enclosed = O x e_o

where e_o = 8.85 x 10^-12 C^2/Nm^2

when the electric field has components Ex = -5.97 N/C and Ey = (4.76 + 2.44y) N/C then the net electric field in xy plane is

E = (Ex^2 + Ey^2)^1/2

the net flux through the surface is

O1 = E x A1

where A1 = 2a^2

Also,

O1 = (q_enclosed/e_o)

or q_enclosed = O1 x e_o

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