Chapter 15, Problem 36RE

As discussed in Example 1 of Section 15.1, Coulomb's law states that the electrostatic force F(r) that a particle of charge Q exerts on a particle of charge q is given by the formula $\text{F}\left(\text{r}\right)=\frac{qQ}{4\pi {\in }_0{‖\text{r}‖}^3}\text{r}$ where r is the radius vector from Q to q and ${\in }_0$ is the permittivity constant.

(a) Express the vector field F(r) in coordinate form $\text{F}\left(x,y,z\right)$ with Q at the origin.

(b) Find the work performed by the force field F on a charge q that moves along a straight line from $\left(3,0,0\right)\text{to}\left(3,1,5\right).$