what is causing the surface charge distribution in simple DC Network? Consider a simple DC Battery and Resistor connected with wire. I know surface charges are responsible for directing the E Field along the wire.But how are these surface charges being moved. There should be the role of battery here but I don't understand how. I would like to know how the E inside battery is changing the E in the wire connected to terminals?
 A: The battery is a body that is able to maintain (more or less) constant difference of electric potential between its two terminals.
According to electromagnetic theory, this potential difference is due to distribution of electric charge on the terminals and inside of the battery. The characteristic behaviour of battery is that it will "try to maintain" non-vanishing charge distribution on its terminals.
Unless other bodies are disturbing the battery, for given voltage, shape and distance of the +/- terminals the macroscopic motion of electric charge elements will cease. From this we know charge ends up in distribution where net force acting on any charge element is zero. The only place where this is possible is surface of the terminals, and only if electric force is perpendicular to it. Very quickly a static equilibrium is established.
When we connect the terminals of the battery to an open circuit and thus close it, the charges on the terminals are no longer bound to terminals and can jump over into the wire.
The new configuration of the system allows for transfer of charges from one terminal to another and the electric field of the battery (with field lines shaped as arcs going from one terminal to another) forces that. The above equilibrium is therefore destroyed.
However, we know that battery can supply constant voltage for quite some time (if the resistance is high enough) and even if current is flowing, the system can be in a sort of macroscopic stationary state. Static circuit will have constant electric current. So after the old equilibrium is destroyed, a new equilibrium must be set up that allows for constant electric potential and constant electric current everywhere.
From Ohm's law we know that in metal where there is current there is also electric field. Constant electric field can only be present near constant charge distribution and it can be shown from EM theory that the only place where non-zero charge density can remain in stationary situation is the surface of the metal. Different places have different density of charge, in order to maintain the stationary situation.
Thus electric charges (both from the battery and the metal) redistribute themselves in such a way that static electric field inside the wires that points along the wire is maintained. This time, the charge elements are not merely on the battery terminals, but on surface of all circuit elements.
The role of the battery in the process of current transfer is to supply (macroscopically) non-electric force inside the battery that keeps the charge elements moving around the circuit. Without the battery, the charges inside the wire would quickly stop their motion due to resistance and they would redistribute in such a way that net electric field inside the wire would vanish. This means mainly the surface charges would redistribute, as they have greatest impact on the electric field inside the wire.
