New solution method for the problem of a uniformly charged straight wire

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A common problem in electrostatics is determining the electrostatic potential due to a uniformly charged straight wire. The solution of this problem illustrates well the types of calculations that one must perform in order to obtain the electrostatic potential or field of a given continuous charge distribution. In this work, we reconsider and solve the problem of a uniformly charged straight wire via a new method that is different from the popular direct integration approach found in the majority of physics textbooks. The outcomes of the two methods are compared and the results suggest several interesting mathematical formulas involving special functions.

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