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 ?


To answer the first question one has to look at the term Electrostatics.

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).
Nothing is balancing the force, so it will then move the charge around. However, that means that our system isn't in equilibrium, since the charge is moving around. In equilibrium, the charges must be at rest, and that can only be the case when there is no electric force along the surface, i.e., when it's perpendicular to it.
Another, looser reason is, the gradient of a scalar field (eg. electrostatic potential) points in the direction of that field's greatest change. No change occurs in the field going along the surface, the gradient should not have a component in that direction.

To answer the second question one has to look at the intuitive understanding of field lines:

The electric field [and force] at a point is tangent to the field line that passes through that point. Does it make sense to you or is further explanation needed?

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  • $\begingroup$ so, the perpendicular is a special case where field lines are perpendicular resulting electrostatics. im interested in the gradient of scalar field explanation, if you could explain or include a link or reference id appreciate that - so the field lines do not represent the field, their tangents represent the resulted field. $\endgroup$ – sarah Apr 17 '17 at 12:12
  • $\begingroup$ 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) $\endgroup$ – Dominik Car Apr 17 '17 at 12:33

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