electromagnetics 2?

Question

A 2microC point charge is located at A(4, 3, 5) in free space. Find Eρ, E φ, Ez at P(8, 12, 2)...show your solution.. thnx

Answer 1

This is much more an exercise in coordinate translation and converting Cartesian coordinates to cylindrical coordinates, than it is an electromagnetics problem.

First translate both A and P back to the origin [A = (0,0,0)]
Then convert the vector P-A from Cartesian to Cylindrical coordinates thus:
x = ρ * cos φ
y = ρ * sin φ
z = z

The E-field is given by:
E = 1 / (4*pi*e0) * (q / r^2)
where:
- pi = 3.141...
- e0 = 8.854E-12 C^2/N*m^2
- q is the charge (2E-6)
- r is the distance in meters

Find the distance from the origin (Aprime) to the translated coordinates at Pprime for X, Y and Z (the 3 'r' values), then apply the formulas for converting to cylindrical coordinates.

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