How come V=El

Consider a positive point +Q charge at the origin O. The work done to move a very small positive charge qthrough a infinitesimally distance dr be dW.

Let the potential at A be V due to the charge +Q at O. thus the potential at a distance dr from O will beV+dV

The work done in moving the charge from B to A in presence of positive charge Q, dW= qdV

The force experienced by the test charge, F = qE , where E is the electric field at B

The work done against this force, dW = -F.dr = -Fdr cos(180)= qEdr

Since the dr is decreasing, dW = -q Edr

Now, dV = -Edr

=> E = -dV/dr