Can two equipotentials ever cross one another? Explain via analogy to a topographical map
Can two equipotentials be tangent to one another? What is the analogous situation in the case of a topographical map?
What is your thinking on this? I will be happy to critique your thinking.
In order to understand if two equipotentials can cross or be tangent to one another, let's first consider an analogy using a topographical map.
A topographical map represents the elevation of a landscape, with contour lines indicating points of equal height. In this analogy, the contour lines represent equipotentials, where each contour line represents points at the same electric potential.
Now, let's examine the first question: Can two equipotentials ever cross one another?
An equipotential line represents points at the same electric potential, just like a contour line on a topographical map represents points at the same height. In the case of a topographical map, it is not possible for two contour lines to cross each other since it would mean that at a single point, there are two different elevations, which is not possible in a physical landscape.
Similarly, in the case of equipotential lines, it would not make physical sense for two equipotentials to cross each other. If they were to cross, it would mean that at a single point, there are two different electric potentials, which contradicts the definition of an equipotential.
Now, let's move on to the second question: Can two equipotentials be tangent to one another?
In terms of the topographical map analogy, two contour lines can be tangent to each other at a single point. This can occur when two adjacent contour lines have the exact same height at that point. It represents a situation where the elevations are equal but can differ slightly at other points.
Similarly, in the case of equipotentials, two equipotential lines can be tangent to each other at a single point. It indicates that the electric potentials are equal at that point but can differ slightly at other points along the lines.
To summarize, in the analogy of a topographical map, two equipotentials cannot cross each other since it would mean two different electric potentials at a single point, which is not physically possible. However, two equipotentials can be tangent to each other, similar to two contour lines being tangent at a single point on a topographical map.