Simplifying the uniform electric field equation

Goatscholar18 · Jan 27, 2018

Homework Statement

Diagram of a uniformly charged thin rod of length L with charge q, points P1 and P2 marked, followed by a worked solution for the electric field at P1 with equations for E(y) at P1 simplified step by step.

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Homework Equations

See Below

The Attempt at a Solution

Handwritten derivation of the electric field of a uniformly charged rod of length L, with the integral of charge density over x from -L/2 to L/2 worked out step by step and a final boxed result of q over 4 pi epsilon zero L times a/2 squared plus x squared expression, with several lines crossed out.

Maybe my answer is right but not simplified enough. But if it is I am having trouble seeing the mathematical equivalency. Please help.

Thanks in advance!

mfb · Jan 28, 2018

Most of that is hard to read, but if you just ask about the answer: Factor out 1/4 in the square root and then get it out of the square root.

TSny · Jan 28, 2018

Also, I don't think you kept track of the factors of a/2 circled below

Handwritten integration of a line charge over a rod from -L/2 to L/2, with the prefactor q over 4 pi epsilon zero L; a substitution gives (x^2 + (a/2)^2)^(3/2) and the antiderivative x over (x^2 + (a/2)^2)^(1/2) evaluated from -L/2 to L/2, with a/2 terms circled in orange.

Simplifying the uniform electric field equation

Homework Statement

Homework Equations

The Attempt at a Solution

Discussion

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