phy electric field line

Just imagine if equipotential lines were not perpendicular to electric field lines, then at any point on an equipotential line, there would be an electric field component pointing in direction along the equipotential line. Such electric field component would drive a charge to move along the equipotential line. This clearly contradicts the definition of equipotential, as there should be no force on the charge along the equipotential line.

Only under the situation that the equipotential line and electric field line are perpendicular to each other, there is no electric field component along the equipotential line, which makes all points on the line to be of the same potential.