### Force between a point and an infinite straight line

Posted:

**Mon Jan 22, 2018 2:55 am**How would I find the force law that describes the force between a point and an infinite straight line g(r), given the force law between two points is f(r)? I have found that simply multiplying f(r) by r only produces the force law g(r) when f(r) is an inverse, or reciprocal law, but if f(r) is something more exotic than an inverse or reciprocal law multiplying f(r) by r does not produce g(r). Also taking the integral of f(r) does not produce the force law g(r), and taking the integral of f(r) divided by r or r^2 does not produce g(r). How can I find the force law g(r) describing the force between an infinite straight line and a point given the force law f(r) describing the force between two points?