D3.6. In free space, let \( \mathbf{D}=8 x y z^{4} \mathbf{a}_{x}+4 x^{2} z^{4} \mathbf{a}_{y}+16 x^{2} y z^{3} \mathrm{pC} / \mathrm{m}^{2} \). (a) Find the total electric flux passing through the rectangular surface \( z=2,0<x<2,1<y<3 \), in the \( \mathbf{a}_{z} \) direction. (b) Find \( \mathbf{E} \) at \( P(2,-1,3) \). (c) Find an approximate value for the total charge contained in an incremental sphere located at \( P(2,-1,3) \) and having a volume of \( 10^{-12} \mathrm{~m}^{3} \) Ans. \( 1365 \mathrm{pC} ;-146.4 \mathbf{a}_{x}+146.4 \mathbf{a}_{y}-195.2 \mathbf{a}_{z} \mathrm{~V} / \mathrm{m} ;-2.38 \times 10^{-21} \mathrm{C} \)
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D = 8 x y z^4 a_x + 4 x^2 z^4 a_y + 16 x^2 y z^3 a_z (units: pC/m^2). (1 pC = 10^-12 C.) Show moreβ¦
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