The figure shows a closed Gaussian surface in the shape of a cube of edge length 2.90 m. It lies in a region where the electric field is given by É = (2.12x+ 2.85)î + 7.37ĵ + 6.22 k N/C, with x in meters. What is the net charge contained by the cube?

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Chapter24: Gauss’s Law
Section: Chapter Questions
Problem 24.63CP: A dosed surface with dimensions a = b= 0.400 111 and c = 0.600 in is located as shown in Figure...
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The figure shows a closed Gaussian surface in the shape of a cube of edge length 2.90 m. It lies in a region where the electric field is
given by É = (2.12x + 2.85)î + 7.37j+ 6.22 k N/C, with x in meters. What is the net charge contained by the cube?
Number
i
Units
Transcribed Image Text:The figure shows a closed Gaussian surface in the shape of a cube of edge length 2.90 m. It lies in a region where the electric field is given by É = (2.12x + 2.85)î + 7.37j+ 6.22 k N/C, with x in meters. What is the net charge contained by the cube? Number i Units
Expert Solution
Step 1

The given electric field is,

Physics homework question answer, step 1, image 1

From the above expression, it is evident that y and z component of the electric field is constant.

Thus, the amount of electric flux coming into the cube along the Y and Z direction is the same as the electric flux going out from the cube in the Y and Z direction.

Thus, the electric field’s Y and Z components do not contribute to the electric flux.

Also, the constant term of the electric field’s x-component does not contribute to the electric flux.

The electric flux can be represented as,

Physics homework question answer, step 1, image 2

Here, da, Q, and ε0 represent the area element, the charge inside the cube, and the free space’s permittivity, respectively.

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