(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

A point dipole p is at the origin of coordinates, while a point charge q is at position r. Calculate the potential energy U of this system in two ways (a) by treating the dipole as a source and q as a test charge in the dipole field (b) by treating the dipole as a test-object in the Coulomb electric field of the point-charge, now treated as a source

2. Relevant equations

U=-pE

V(r)=Integral of Edr

3. The attempt at a solution

I found the potential

V(r)=p.r/(4πε0r^3)=p.r(hat)/(4πε0r^2)=pcosθ/(4πε0r^2)

Then I differentiated since E(r)=d/dr(V(r))

E(r)=-d/dr(V(r))=-d/dr(pcosθ/(4πε0r^2))=-(-3pcosθ/(4πε0r^3))=3pcosθ/(4πε0r^3)

So my U would be equal

U=-pE=-p(3pcosθ/(4πε0r^3))=-3p^2cosθ/(4πε0r^3) ????

It doesn't make sense

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# Homework Help: Potential energy of a dipole point and point charge

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