How electric field lines are drawn

Two Questions:

1. Field lines are always drawn perpendicular to the surfaces at the point of contact, what does that say about the physical electric field ( or why are they drawn as so not with an angle or parallel or otherwise. )

2. If ( according to my understanding ) field lines are lines of forces that represent the possible force effect of its charge in space , then what do the tangents to them represent ?

Let's say that the field is not perpendicular to the surface. That means it has a component along the surface $->$ so now we have a force on the charges in the conductor along the surface of the conductor (no longer electrostatics).
• Yes, in electrostatics. en.wikipedia.org/wiki/Gradient You know that the derivative is the amount of change of the variable. Gradient takes a scalar and turns it into a vector showing the greatest rate of change. You know that there is no change in the field when you are perpendicular to it, so the gradient is $0$, and that only happens when the dot product is $0$, and the dot product is $0$ for perpendicular vectors (90 degrees, or $\pi/2$ radians) – Dominik Car Apr 17 '17 at 12:33