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, Technology Update (No access codes included)
9th Edition
ISBN:9781305116399
Author:Raymond A. Serway, John W. Jewett
Publisher:Raymond A. Serway, John W. Jewett
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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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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