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A straight line segment has a length L that carries a uniform line charge lambda which...

A straight line segment has a length L that carries a uniform line charge lambda which extends from z = 0 to z = L.

A) Calculate the potential a distance z from the origin. Assume that z > L.

B) Calculate the electric field from the potential.

C) Show that the electric field from the line charge falls off essentially as a point charge (so 1/z^2) as z gets large and a charge of lambda*L in the z-direction using a Maclarin Series expansion (using a typical form of (1+x)^n where x is small) to approximate the square root term.

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