If you want to calculate the electric field at a distance r from a line of infinite length and uniform charge density you could one of three things:(adsbygoogle = window.adsbygoogle || []).push({});

1. Employ symmetry and Gauss' law.

2. Use superposition and integrate from minus to plus infinity along the rod.

3. Integrate to find the potential and differentiate.

1. and 2. work fine and unsurprisingly give the same result. But when I try 3., I get an integral of the form:

[tex]\int^{\infty}_{-\infty} \frac{b ds}{\sqrt{a^2 + s^2}}[/tex]

Equal to an inverse sinh, which diverges, surely impossible to differentiate. Why is this?

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Convergent field, divergent potential?

**Physics Forums | Science Articles, Homework Help, Discussion**