# Charge flow is impeded(Expansion – lead me deeper)

One the circuit is up and running then there is a steady flow of charge, but the battery is needed to maintain that flow. As the flow is steady the average resultant force on a moving charge must be zero. That is the retarding forces and the driving forces must be equal.

Because the conductors making up the circuits are electrically neutral, and there are charged particles drifting along in one direction, there must be fixed charged particles of opposite sign in the wires.

As the moving charged particles move through this array of fixed charged particles, there will be interactions. There are electrical forces between two charged particles (see the SPT: Forces topic). These will vary over time as the charged particles drift closer to or further away from the fixed charged particles, but we'll take an average value to make a simple model. But if the wire is the same everywhere around the circuit, then the magnitude and direction of the force on the moving charged particles must be the same–always opposing the steady drifting motion of the charged particles. What else could it be?

The battery therefore needs to exert a constant average force on each charge, equal and opposite to the retarding force, wherever the charge is in the circuit. This driving force must be along the axis of the conductor, aligned with the current. As the battery has a positive and negative end, (it's a chemical charge pump), the driving force acting on the charge is again electrical. And as the drifting speed of the moving charged particles is constant everywhere in the circuit, so the average driving force must be the same everywhere in the circuit.

### The action of the battery

So the concentrations of charged particles on the battery drive the charged particles around the circuit. But just how do they do this?

It cannot be simply that there is a great concentration of charge on the positive terminal and this exerts the force. There are two good reasons why the current cannot be explained by just referring to a concentration of charged particles on the terminal.

The force acting on the moving charge would get smaller, the further the charge gets from the battery–and we have just found that it needs to be constant everywhere so that the resultant force on the moving charged particles is zero everywhere.

The force provided by the battery needs to be aligned with the conductor–however many bends we put in the conductor.

Nor can it be the case that it is just the like (moving) charged particles repelling, as the body of the conductor is, and remains, electrically neutral. Therefore, on average, any moving charge in the body of the conductor will be surrounded by opposite charged particles closer to it than its nearest similar charge. These opposite charged particles, being closer, will exert much larger forces on the moving charge than its nearest moving charged particles.

So here is what does happen.

The battery sets up a distribution of charged particles on the outside of the conductor, and these charged particles exert the driving forces on the moving charged particles.

It does take a very short time for the distribution of charged particles to be set up, with all kinds of feedback loops operating over very short timescales (the electromagnetic signals carrying the information about how to set up this charge distribution travels at the speed of light).

The distribution of charged particles then exerts forces on the flowing charged particles, so causing the varying drift velocities in the different parts of the loop. The velocities will not be constant because:

• There must be changes of direction to make a loop.
• The charged particles move at different speeds in different parts of the loop (although the current is the same in each part of the loop).
• ### Varying the elements in the circuit

Now the model needs refining, to explain why some parts of the circuit glow and others do not. Here we'll focus on wires, but the same arguments are true for any conductor.

As you will have noticed, filaments in bulbs are simply very thin wires, so let's build a very simple circuit, where one section of the wire is thinner–that's the only change.

Firstly let's focus on what happens to the charged particles, comparing their motion in the thick wire to the motion in the thin wire. For simplicity we'll make the two wires of similar material–so everything is the same, apart from the thickness of the wire, and so the cross sectional area.

It does not take much thinking to see that the charged particles must move faster in the thinner wire, to avoid a steady buildup of charge at one end, and a steady loss of charge at the other. This is a simple consequence of the charge not getting lost or used up on the way round the circuit loop. Charge is conserved.

(An aside–this is really just a transport problem–we're modelling the charged particles as a kind of incompressible fluid. Very similar models are used for traffic and pedestrian flow, not to mention rivers and glaciers.)

What is the effect of this faster movement in the thinner wire on the forces acting on the moving charged particles? You can figure this out for both the retarding forces and the driving forces (remember that these must be equal). Again it's not hard to reach the conclusion that the forces in the thinner wire must be larger. The moving charged particles maintain a steady higher speed, and so interact with more fixed charged particles each second. More interactions lead to a larger average retarding force, and so a larger average driving force.

### Why some parts glow

The filament glows and the connecting wires in the circuit do not. Why?

You have found that the forces acting on the moving charged particles by the battery and by the fixed charged particles in the filament are larger.

A larger force acting for a similar distance shifts more energy (See the SPT: Energy topic). So, for each metre or centimetre or millimetre of filament wire that the charged particles travel along, the large forces acting on them shift lots of energy: for each metre or centimetre or millimetre of connecting wire that the charged particles travel along, the very small forces acting on them shift a tiny quantity of energy.

The retarding force shifts energy to the thermal stores of the surroundings.

The driving force shifts energy from the chemical store of the battery.

The quantities of energy shifted are identical, because the driving and retarding forces are identical.

To increase the energy shifted, increase the speed of the charged particles by decreasing the thickness of the wire.