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Show that the family of right circular cones $$ x^{2}+y^{2}=c z^{2} $$ where $c$ is a parameter, forms a set of equipotential surfaces, and show that the correspond...

Question

Show that the family of right circular cones $$ x^{2}+y^{2}=c z^{2} $$ where $c$ is a parameter, forms a set of equipotential surfaces, and show that the corresponding potential function is of the form $A \log \tan \frac{1}{2} \theta+B$, where $A$ and $B$ are constants and $\theta$ is the usual polar angle.

Show that the family of right circular cones $$ x^{2}+y^{2}=c z^{2} $$ where $c$ is a parameter, forms a set of equipotential surfaces, and show that the corresponding potential function is of the form $A \log \tan \frac{1}{2} \theta+B$, where $A$ and $B$ are constants and $\theta$ is the usual polar angle.



Answers

Show that the parabolas $ r = c/(1 + \cos \theta) $ and $ r = d/(1 - \cos \theta) $ intersect at right angles.


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