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Electric Fields (Line, Loop and Disc)

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Would you please help me to understand the following questions?

(1) Consider a line of charge, density ?, length L, lying along the x-axis from 0 to L. Find the electric field E a distance z along the z-axis. What is the limiting value when z >> L ?

(2) Find the electric field, E a distance z above a circular loop of charge, radius r, in the x â?' y plane centered on the origin. What is the limiting value for z>> r ?

(3) Find the electric field, E a distance z above a disc of radius R and surface charge Ï?. Describe the limits Râ?'â??and z >> R.

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The expert examines electric field line, loops and discs.

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Hello and thank you for posting your question to Brainmass!

The solution is attached below in two files. the files are identical in content, only differ in format. The first is in MS Word format, while the other is in Adobe pdf format. Therefore you can choose the format that is most suitable to you.

Note that for problems 2 and 3 I assumed you wanted the electric field along the z axis and not at any point in space. Off-axis field of a disk and a loop is not that simple and require solving the Laplace equation in spherical coordinates and then taking the gradient of the potential, which is in series form.

The system looks like:

We divide the line into infinitesimal segments of length dx, each carrying a charge of
Therefore, the ...

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