Points A and B are arbitrarily located in a uniform electric field that extends
ID: 2052905 • Letter: P
Question
Points A and B are arbitrarily located in a uniform electric field that extends throughout all of space. Your friend claims, "Whether you stand at A or at B, your surroundings are identical. In other words, the field looks the same from every point in space, so no point is different from any other. Therefore, the electric potential should be the same everywhere in space, no matter where you are. There can be no potential difference between any two points A and B." The conclusion is wrong, so what is the flaw in your friend's argument?Explanation / Answer
The flaw is that potential is never measured at a point, it is undefined at a point. Potential exists only as the difference between two points. It is true that the field looks the same everywhere. But the entire reason the field exists is that the scalar potential between two points differs.
E = -grad is the definition of the vector E; the gradient of a scalar field can be a constant vector everywhere and yet the scalar itself differs at different points.