Calculus 3: Work Homework: Electric Dipole Field

[tarantino5]

Homework Statement

An electric dipole with dipole moment p = 4 × 10−5 C-m sets up
an electric field (in Newtons per coulomb)

F(x,y,z) = $kp/r^5$ <3xz, 3yz, 2z$^{2}$ - x$^{2}$ - y$^{2}$>

where r = (x$^{2}$ + y$^{2}$ + z$^{2}$)$^{1/2}$ with distance in meters and k = 8.99 ×
109 N-m$^{2}$/C$^{2}$. Calculate the work against F required to move a particle
of charge q = 0.01 C from (1,−5, 0) to (3, 4, 4). Note: The force on
q is qF Newtons.

Homework Equations

∫$^{b}_{a}$ F(c(t)) * c'(t) dt

The Attempt at a Solution

I know that I need to set ∇f = F and find a potential function. I'm not sure what the parametric equation should be.

 

[clamtrox]

I know that I need to set ∇f = F and find a potential function. I'm not sure what the parametric equation should be.

Perhaps you don't need to calculate the potential at all. Seems like you get work directly from the force, according to your formula.

The path parametrization depends on the path of course. It seems a path is not specified in the problem. Why is it not needed to solve the problem?