Question

Can two equipotential lines cross? Why or why not?

Short answer

Why or why not? Answer: No, two equipotential lines cannot cross or intersect each other. This is because each point in a potential field, such as an electric field, can have only one unique potential value, and equipotential lines represent points of equal potential. Intersecting equipotential lines would imply a violation of this basic principle, as a single point would have two different potential values.

Step-by-step solution

Equipotential line definition

Equipotential lines are lines along which the potential (e.g., electric potential) is constant. This means that all points on the line have the same potential value. Since the potential is constant, there is no work done in moving a charge along an equipotential line.

Unique potential value per point

In any potential field, each point can have only one unique potential value. Thus, two different equipotential lines cannot have the same value of potential at any given point.

Non-intersecting equipotential lines

Since each point in a field can have only one unique potential value, it means that two equipotential lines with different potentials cannot intersect or cross each other at any point. If two equipotential lines were to intersect, it would mean that a point is simultaneously at two different potential values, which is not possible.

Conclusion

No, two equipotential lines cannot cross or intersect each other. This is because each point in a potential field, such as an electric field, can have only one unique potential value, and equipotential lines represent points of equal potential. Intersecting equipotential lines would imply a violation of this basic principle, as a single point would have two different potential values.