Equal potential lines question.?

Question

why are electric field lines perpendicular to the equipotential lines?

Answer 1

An electric field  is related to the potential as follows :

E = - grad V .

            Equipotential lines have constant potential & hence the tangential component of the field is null. The field is normal to the equipotential lines.

Answer 2

if a charge is moved along a electric field work is done

w=q*dV

but if a charge is moved along a equipotential surface no work is done because dV is zero

if there is a tangential component dV wont be zero cause E=-dv/dr