# Can't find Potential Difference of Charge in Electric Field

I'm trying to find the potential difference of a punctual charge $Q=-3\mu C$ that moves from cartesian coordinate A(1,1,-1) to B(2,2,-1) in the external electric field $$\vec{E}=\left[ \frac{z}{x^2y}, \frac{z}{xy^2}, -\frac{1}{xy}\right].$$

So far I tried this:

\begin{align*} V_{ba} &= - \int_a^b \vec{E} \cdot d\vec{L}\\ &=-\int_1^2 \left[ \frac{z}{x^2y}, \frac{z}{xy^2}, -\frac{1}{xy}\right] \cdot \left[dx,0,0 \right]-\int_1^2 \left[ \frac{z}{x^2y}, \frac{z}{xy^2}, -\frac{1}{xy}\right] \cdot \left[0,dy,0 \right]\\ &=\frac{-z}{2y} - \frac{z}{2x}. \end{align*}

I dont know how to interpret this result. Am I making a mistake ?

• So , like this ? $-\int_1^2 \frac{-1}{x^2}dx -\int_1^2 \frac{-1}{y^2}dy$ – Liam F-A Mar 2 '18 at 4:28