Hi, Please answer the following question below: The Gaussian cube in the figure

Question

Hi, Please answer the following question below:

The Gaussian cube in the figure below has edge length a = 2.0 m. The cube is in a region filled with a uniform E-field given by = 2 - 4 + 5 N/m. For each of the 6 faces of the cube show the area vector . Notice that on each face, is closely related to one of the Cartesian unit vectors. For example, on the left face = -4 where 4 is the area of the face. Calculate the electric flux through each face. (Left, Right, Top, Bottom, Front, Back.) What is the net (total) flux? Use the concept of the Gauss law to explain why your answer to part (c) makes sense.

Explanation / Answer

a)

Left: -4j

Right: 4j

Top: 4k

Bottom: -4k

Front: 4i

Back: -4i

b)

electric flux = E.A =

Left: flux = E.A = (2i - 4j + 5k).(-4j) = 16 N.m2/C

Right: flux = E.A = (2i - 4j + 5k).(4j) = -16 N.m2/C

Top: flux = E.A = (2i - 4j + 5k).(4k) = 20 N.m2/C

Bottom: flux = E.A = (2i - 4j + 5k).(-4j) = -20 N.m2/C

Front: flux = E.A = (2i - 4j + 5k).(4i) = 8 N.m2/C

Back: flux = E.A = (2i - 4j + 5k).(-4i) = -8 N.m2/C

c)

total flux = 16 + (-16) + 20 + (-20) + 8 + (-8) = 0

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