Why doesn't charge accumulate in a loop?

Question

When learning about electromagnetism at my university, electricity flow is generally shown as a conductor with a high potential at one end and a low potential at the other and thus charges flowing down that potential gradient.

The charges are said to accumulate at one end until their own potential flattens this gradient.

We are then taught that this accumulation does not occur in a loop but I don't understand why it wouldn't.

At some point in the loop won't the charges necessarily have to go up a potential gradient to travel around the whole loop? If this is done by some mechanism in a battery does that mean it is incorrect to state that all you need for current flow is a closed loop of conductor and a pd?

Also current flow isn't the movement of charge but the movement of signal or fields if I understand correctly. So how is current flow in a non loop stopped so quickly?

I am a physics student with a pretty poor understanding of circuit components etc so if this can be explained with electromagnetic principles more than circuits I would really appreciate it, though no worries if not!

Thanks so much

Answer 1

It depends on how this potential difference is applied to the conductor. The first case seems to correspond to a conductor placed in an external electric field. Then the charges would move to the ends of the conductor and build up a counteracting electric field so that the field and potential difference and thus the current in the conductor becomes zero. This is a consequence of the charge flow being blocked at the ends. The same would happen to a conducting loop that is placed in an external field. Opposite charges would build up at the end of the loop in the direction of the applied external field. The situation is different when the potential difference is due to an applied battery which maintains a potential difference at the ends of a conductor. Then a constant current flow occurs because the charge entering the conductor from the battery at one electrode flows back through the conductor entering the battery at the other electrode where it continues to the other electrode. Thus the charge current flow forms a circuit and there is nowhere an accumulation of charge due to this current. Similarly, a closed conductor loop in a changing magnetic field, which produces an electric field by induction along the loop, has a current without an accumulation of charge. This is a consequence of the law of charge preservation, or the current continuity equation in the stationary case.

Answer 2

Consider a simple DC circuit with a battery, highly conductive wires and a resistor. A current will flow in the circuit and if the battery create a potential difference V, and the total resistance of the circuit is R, a current I = V / R will flow in the circuit. But how does the flux of charges follow the shape of the circuit?

The answer is that charge will accumulate (in general in a very complicated way) on the surface of the conductor (and the resistor) in order to provide an electric field that, once superposed to the electric field that would be generated by the battery alone, will produce a resultant field Etot that is directed along the conductor and satisfies Ohm's law in its local form j = sigma Etot, inside the conductor.

Also, charge will accumulate at the interfaces between materials with different conductivity and permeability, and in particular at the resistor's interfaces with the highly conductive wires.

In the end, once an initial very fast transient is over, you will have a small, almost negligible electric field (resulting in a negligible voltage drop) in the copper wires, whereas inside the resistor - thanks to the charge accumulated at its ends - there will be a much stronger electric field (that accounts for the big voltage difference we see across R).

See the figures in this answer to see a circuit with lumped resistors and also a circuit with a battery connected to an homogeneous resistive loop. In the latter case you will see charge accumulation at the interfaces between battery and resistive loop but also charges on the entire surface of the loop. In this conservative field example, the electric field lines along which the seeds are oriented, start from positive surface charges and end in negative surface charges.

For an accessible introduction see Chabay and Sherwood, "A unified treatment of electrostatics and circuits" published on the American Journal of Physics, and also their textbook "Matter and Interactions".