## Coulomb Force Between A Charge Rod & A Particle

Hi All,

I have a simple physics question, which I wonder if somebody could help
me with as I am a computer science person trying to use Coulomb force as
an error metric.

In 3D space, if I have a charged rod, (length l with start and end
points, r1 and r2) and an oppositely charged particle positined at p1,
what is the coulomb force between them?

I am assuming you have to integrate the standard coulomb force between
two particles along the rod (Excuse the poor english),

Any help is much appreciated,

 "Adam Teasdale Hartshorne" a écrit dans le message de news: ed4ndk$stj$1@mail.dcs.warwick.ac.uk > I have a simple physics question, which I wonder if somebody could help > me with as I am a computer science person trying to use Coulomb force as > an error metric. > > In 3D space, if I have a charged rod, (length l with start and end > points, r1 and r2) and an oppositely charged particle positined at p1, > what is the coulomb force between them? > > I am assuming you have to integrate the standard coulomb force between > two particles along the rod (Excuse the poor english), The result depends on only two variables: the radial distance between the point and the rod, and the axial distance. Let's take a reference frame X, Y, Z such that the rod is along the Z axis and centred at the origin, thus starting at z = -l / 2 and ending at z = l / 2. If x, y, z are the coordinates of the point, the radial and axial distance are respectively r = sqrt(x^2 + y^2) and h = z. Each infinitesimal element of the rod gives a force which radial and axial components are: dF_r = k r dz / sqrt((h-z)^2 + r^2) / ((h-z)^2 + r^2) dF_a = k (h-z) dz / sqrt((h-z)^2 + r^2) / ((h-z)^2 + r^2) Finally the total force is their integral over z between -l / 2 and l / 2 F_r = k r Int dz / ((z-h)^2 + r^2)^3/2 F_a = k Int (h-z) dz / ((z-h)^2 + r^2)^3/2 Combining them, the force is: F = sqrt(F_r^2 + F_a^2) Good luck. Your may also consider an infinite rod. It is then much simpler since the axial component is zero and the force is proportional to 1 / r. -- ~~~~ clmasse on free F-country Liberty, Equality, Profitability.