A rod of length l located along the x axis has a total charge Q and a uniform linear charge density lambda = Q/l. Find the electric potential at a point P located on the y axis a distance a from the origin.

This is a classic problem to solve when the electric potential of continuous charge distributions is studied. It is not fantastic. but it serves as a cornerstone to solve increasingly complex problems. we will solve it!
The length element dx has a charge dq = (lambda)dx. Because this element is a distance r = sqrt(x^2 + a^2) from point P, we can express the potential at point P due to this element as:

To obtain the total potential at P, we integrate this expression over the limits x = 0 to x = l. Noting that ke and are constants, we find that:

such integrals are solved by trigonometric change. to simplify things we will solve the indefinite integral and then evaluate the result in the limits:

Evaluating V, we find that

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