Question

calc 3 question! need help quickly!!!


Find the potential function for
F(x,y,z)= <(-cx/((x^2)+(y^2)+(z^2))), (-cy/((x^2)+(y^2)+(z^2))), (-cz/((x^2)+(y^2)+(z^2)))>
Prove!

Answer 1

Except at (0,0,0), the potential function is
\[
-\frac{1}{2} c \log
\left(x^2+y^2+z^2\right)
\]
Just take its gradient and see that is equal to your field.