Electrical engineering. Solving an electrical engineering problem. (Coursework Sample)

Electrical Capacitance
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1. A charge, Qo, is located in free space (εr= 1) and can be assumed to form the origin of a rectangular coordinate system as shown in Figure 1. This charge produces an electric field strength for which Ez= 1.5kV/m at a point P1 (-2, 1,-1).
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Figure SEQ Figure \* ARABIC 1 Rectangular grid of Q1
Find:
a. The charge Qo. (Coulombs)
The field at point P = Ep = (Q02/ 4πt0) – (Zax + ay – az2)62S
This is because z is an element of the value 1kv per m.
Therefore:
Q = -4nt0 * 6^1.5 * 10^3 = 163µC
b. E at a second point P2 (1, 6, 5) in rectangular coordinates (V/m).
E at M (1, 6, 5) in the Cartesian coordinates
The field is:
EM= (-163 / 4 * π to) * 10^62(ax + 6ay + 5az) ^ 3 / (1 + 36 + 25) ^1.5
αEM = -30.11ax – 180.63ay – 150.53az
c. E at P2 in spherical coordinates (V/m).
Finding E at M (1, 6, 5) in spherical co-ordinates:
At M, r = 1 + 36 + 25 = 7.87
ϕ= 80.54 and θ = cosϕ-1(5 / 7.87) = 50.58
Because the charge is at the origin, we can only get the radial component EM, which will be:
Er = EM * ar = -30.11 * sin θcosϕ– 180.63 * sin θsinϕ– 150 * cosθ = 237.1
d. An equal but opposite charge, -Qo, is introduced at P2, what is the force and its direction on this new charge?