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A cube 2 m on a side is located in the first octant in a Cartesian coordinate system, with one of its corners at the origin. Find the total charge contained in the cube if the charge density is given by ρv = xy2e−2z (mC/m3).
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The total charge contained in the cube for the given conditions.
Answer to Problem 1P
The total charge contained in the cube for the given conditions is
Explanation of Solution
Given data:
The side of the cube is
The volume charge density is
Calculation:
The required diagram for the given condition is drawn as shown in Figure 1.
Write the standard expression of charge for volume charge density.
Here,
Differential volume in Cartesian coordinate system is,
The given cube is resting on one of its corner at origin and in the first quadrant.
Hence, range of
Range of
Range of
Substituting
Solve the above expression.
Conclusion:
Therefore, the total charge contained in the cube is
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Chapter 4 Solutions
Fundamentals of Applied Electromagnetics (7th Edition)
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