If D = (2y² + z)a¸ + 4xya, + xa₂ C/m², find (a) The volume charge density at (−1,0,3) (b) The flux through the cube defined by 0 ≤ x ≤ 1,0 ≤ y ≤ 1,0 ≤ z≤ 1 (c) The total charge enclosed by the cube

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PRACTICE EXERCISE 4.8
If D = (2y² + z)ax + 4xya, + xa₂ C/m², find
(a) The volume charge density at (-1,0,3)
(b) The flux through the cube defined by 0 ≤ x ≤ 1, 0 ≤ y ≤ 1,0 ≤ z ≤ 1
(c) The total charge enclosed by the cube
Answer: (a) -4 C/m³, (b) 2 C, [(c) 2 C.
Transcribed Image Text:PRACTICE EXERCISE 4.8 If D = (2y² + z)ax + 4xya, + xa₂ C/m², find (a) The volume charge density at (-1,0,3) (b) The flux through the cube defined by 0 ≤ x ≤ 1, 0 ≤ y ≤ 1,0 ≤ z ≤ 1 (c) The total charge enclosed by the cube Answer: (a) -4 C/m³, (b) 2 C, [(c) 2 C.
Expert Solution
Step 1

The density of the charges at a certain location is referred to as the charge density. Charge per area is represented by surface charge density, while charge per volume is represented by volume charge density. Charge densities are constant for homogenous charge distributions.
The total flux traveling through the cube would be zero if the frame of reference were at the cube's centre, and as a result, the charge contained within the cube would also be zero. The total of the electric fluxes via the six faces makes up the net electric flux through the cube.

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