Electric Potential

Electric potential is potential energy per unit charge, $V = U/q_0$, measured in volts, which are joules per coulomb. For a point charge $V = kq/r$, with the sign of $q$ kept, and several charges superpose by plain signed addition of $kq_i/r_i$. The field is recovered as the negative gradient, $E_x = -dV/dx$: the field is the SLOPE of the potential. Surfaces of constant $V$ are equipotentials, motion along them costs no work, and field lines pierce them at right angles. Because the electrostatic field is conservative, $\Delta V$ between two points depends only on the endpoints and never on the route.

Five errors dominate. Treating $V = 0$ and $E = 0$ as the same claim, when midway between $+q$ and $-q$ the potential is zero and the field is strong, and midway between two $+q$ the field is zero and the potential is large. Resolving potentials into components or letting two contributions partially cancel by geometry, when the only cancellation available to a scalar is between opposite signs. Exporting $E = V/d$ out of the uniform field it was derived in, which the point charge disguises because $E = V/r$ happens to hold there. Charging work for motion along an equipotential, or drawing field lines that cross contours obliquely. And letting the potential difference depend on which route was taken.