Q:

Can two equipotential lines cross?

A:

Two equipotential lines cannot cross. These lines are perpendicular to the electric force, and the electric force at a point in space can only point in one direction. Equipotential lines can be considered to be similar to the contour lines on a map, which also never cross.

Another way in which the equipotential lines are similar to contour lines on a map is when considering work done by a force. An object traveling along an altitude contour line would not have to do work against the force of gravity. Similarly, equipotential lines are perpendicular to the electric force, so charges that travel along the equipotential line do not need to do any work against the electric force.

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