# Voltage Due to Charge Configuration

See the attached file.

Let a uniform surface charge density of 5 nc/m2 be present at the z=0 plane, a uniform line charge density of 8 nc/m, be located at x=0, z=4 and a point charge of 2 μC be present at P(2,0,0). If V=0 at M(0,0,5), find V at N(1,2,3).

It seems to me that I need to find the electric field intensity for each of the charge configurations (the surface charge, the line charge, and the point charge), add the components (changing between coordinate systems where necessary), and then compute the integral. However, I do not understand how to find expressions for the electric field intensity or how to adjust the calculations if the zero reference potential is not at infinity.

In summary, please explain:

1. How to derive the electric field intensity for each of the charge configurations (with particular emphasis on line charges that are not parallel to the z-axis)

2. What difference it makes that the zero reference is not an infinity

3. How to obtain the final answer (please show vector operations in detail as that is often where I get lost)

This problem has stumped me for a week now. Many thanks for your help.

#### Solution Preview

See attached file for solution.

Let a uniform surface charge density of 5 nc/m2 be present at the plane, a uniform line charge density of 8 nc/m, be located at , and a point charge of 2 μC be present at P(2,0,0). If at M(0,0,5), find V at N(1,2,3).

(answer is 1.98 kV)

It seems to me that I need to find the electric field intensity for each of the charge configurations (the surface charge, the line charge, and the point ...

#### Solution Summary

This post provides a solution for electric field intensities for charge configurations (surface charge, line charge, and point charge).