The potential difference and electric field are related by

$\overline{){\mathbf{-}}{\mathbf{\u2206}}{\mathbf{V}}{\mathbf{=}}{\mathbf{E}}{\mathbf{\u2206}}{\mathbf{r}}}$

where Δr is the distance between charges and the negative sign indicates direction.

The electric potential due to a point charge is

$\overline{){\mathbf{V}}{\mathbf{=}}\frac{\mathbf{kq}}{\mathbf{r}}}$

The electric field due to a point charge is

$\overline{){\mathbf{E}}{\mathbf{=}}\frac{\mathbf{kq}}{{\mathbf{r}}^{\mathbf{2}}}}$

1. If the electric potential at some point is large, is the electric field at that point also necessarily large, or not? Explain your answer, and provide a counterexample if not.

2. Assume the electric field E in some region is uniform: it is the same at all points. Specifically, E has a magnitude of 5 V/m and points in the +x direction. What can you then say about the behavior of the electric potential a) in the x direction and b) in the y direction? Explain your answers.

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