The potential difference and electric field are related by
where Δr is the distance between charges and the negative sign indicates direction.
The electric potential due to a point charge is
The electric field due to a point charge is
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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