Question

Let D = 20 x.y3 .z4 ax + 30 x2 .y2 .z4 ay + 40x2 .y3 .z3 az C / m2 . a) What is the load contained in a volume of 10-10 m3  located at (3, 1, 2)? b) What about (2, 2, 3)? (c) At which point in the region 0 ≤ x ≤ 3, 0 ≤ y ≤ 3, 0 ≤ z ≤ 3, is the maximum quantity flow through the 10-10 m3 incremental volume , and what is ∆Ψmax?
Answer:
(a) 1,328 µC; (b) 8,64 µC; (c) P(3, 3, 3), 43,7 µC.

Answer 1

The charge density is given by

Total charge =

a) At (3,1,2), with V = 10^-10 m³,

b) At (2,2,3), with V = 10^-10 m³,

c) Since the function D is increasing function for x,y and z,(no negative signs in equation), the maxima point for ant interval will be the point with maximum (xyz) values.

For the interval in the question, this point is (3,3,3)

d) At (3,3,3), with V = 10^-10 m³,