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?

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?

Physics for Scientists and Engineers: Foundations and Connections

1st Edition

ISBN:9781133939146

Author:Katz, Debora M.

Publisher:Katz, Debora M.

Chapter25: Gauss’s Law

Section: Chapter Questions

Problem 48PQ

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Concept explainers

Electric Charges and Fields

One of the fundamental properties is the electromagnetic property. Charge cannot be destroyed by any process and this contributes formally to the law of charge conservation.

Question

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,

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,

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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