A straight rod of length L has a positive charge Q distributed along its length.

Question

A straight rod of length L has a positive charge Q distributed along its length. Find the electric potential due to the rod at a point located a distance dd from one end of the rod along the line extending from the rod.

Choose a coordinate system where +x is to the right and +y is upward. Place the origin of your coordinate system at the left end of the rod, and choose point P to be located beyond the right end of the rod, as shown in the picture to the left.

What is the distance ri between point P and a piece of charge located at position xi ?

Express your answer in terms of some or all of the quantities xi , L , Q , and d .

Explanation / Answer

the electric field is

E = k x (q/L^2 + d^2))

where k = (1/4pi x e_o) = 9 x 10^9 Nm^2/C^2 and q is charge on the rod

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