Why we don't draw electric field lines through conductors?
a little bit of confusion in the question But i am providing answers for both the possible outcomes
Question should be Electric field inside a conductor or why is not the electric field donot form closed loop ?
In the case of first question which i assume
In electrostatics free charges in a good conductor reside only on the surface. So the free charge inside the conductor is zero. So the field in it is caused by charges on the surface. Since charges are of the same nature and distribution is UNIFORM, the electric fields cancel each other.
The Second question why is not the electric field donot form closed loop ?
For a positive charge, the electric lines of force will be radially outward, and for a negative one, they will be radially inward.
Also, electric lines of force originate from a positive charge and terminate at a negative charge.
Thus, if we consider that a single line of force emerges out of a positive charge and loops back to the same point from where it originated, it would mean that there are two charges placed exactly at a same point, which is nonsensical.
Also, an electric line of force represents the direction in which a unit positive charge would move if placed along the line. So, in this case the positive charge should be repelled and then should come back towards the source charge, which would not be digestible.