Concept explainers
Assume the magnitude of the electric field on each face of the cube of edge L = 1.00 m in Figure P23.32 is uniform and the directions of the fields on each face are as indicated. Find (a) the net electric flux through the cube and (b) the net charge inside the cube. (c) Could the net charge he a single point charge?
Figure P23.32
(a)
The electric flux through the cube.
Answer to Problem 24.32P
The electric flux through the cube is
Explanation of Solution
The length of the edge of the cube is
The area vector is always out of face. The electric field going into the face of the cube makes
Write the expression for total flux through the cube
Here,
Write the area of the cube
Here,
Substitute
Here,
Conclusion:
Substitute
Therefore, the electric flux through the cube is
(b)
The net charge inside the cube.
Answer to Problem 24.32P
The net charge inside the cube is
Explanation of Solution
The length of the edge of the cube is
Write the expression for flux through the cube by Gauss law
Here,
Conclusion:
Substitute
Therefore, the net charge inside the cube is
(c)
The number of charges inside the cube.
Answer to Problem 24.32P
The net charge is not a single point charge.
Explanation of Solution
The electric charge is the physical property of the matter that causes it to experience a force when placed in an electromagnetic field.
The net charge is not a single point charge as it does not produce a uniform field on the face of cubes. The equipotential surface of the single point charge is spherical. So the net charge is not a single point charge.
Conclusion:
Therefore, the net charge is not a single point charge.
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Chapter 24 Solutions
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