Chapter 14.5, Problem 60E

Electric potential The potential function for the force field due to a charge q at the origin is $\phi =\frac{1}{4\pi {\epsilon }_0}\frac{q}{\left|r\right|}$, where r = 〈x, y, z〉 is the position vector of a point in the field and ε₀ is the permittivity of free space.

a.    Compute the force field F = – ▿φ

b.    Show that the field is irrotational; that is ▿ × F = 0.