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[itex]W=\int_{\mathbf{r_1}}^{\mathbf{r_2}} \mathbf{F} \cdot \mathbf{dr}[/itex]

which ends up giving W=qV where V is the potential difference.

However in previous years we used [itex]\mathbf{F}=-\nabla W \Rightarrow W=-\int_{\mathbf{r_1}}^{\mathbf{r_2}} \mathbf{F} \cdot \mathbf{dr}[/itex]

(this works if you consider W as potential energy (mgz) and then you get a force due to gravity of -mg in the z direction.

so which is correct and why?