# Energy direction in an electronic circuit

I've been reading a number of materials trying to understand the physics that allow electricity to be possible. I'm confused by this virtual positive [charged] particle (often called a test particle) that is used to explain the direction/properties of an electric field and thus the movement of energy in a circuit.

Specifically, I recognize that the energy is loaded onto this virtual positive particle by the virtue that Work and thus a gain of Energy is required for the positive particle to move from the anode side of the battery back to the cathode side of the battery (where the energized ions are present). From this point the positive particle (now energized and at the point of high energy at the cathode) move to the point of low energy (the anode) offloading their energy onto a load which transforms it into some other form of energy (thermal in the case of a short circuit or resistor load).

I'm curious though how does this positive particle move in any direction? With a classic electronic circuit (copper wires) the electrons are the charge carriers and thus form the charge highway/sea of electrons allowing energy to move (in response to a induced electric field). i.e electrons move, atoms/ions do not.

Is this simply a convention (much like conventional current vs electron current) in that the ions are not moving but the illusion is given that they are by virtue of the electrons moving and leaving holes/positive charges in their wake (in the opposite direction)? Is so why was it chosen instead of using a negative charged particle and thus being easily traceable by the movement of electrons?

• Batteries are exoelectric electroplating systems. – Ignacio Vazquez-Abrams Jul 17 '14 at 4:07
• I recognize that the battery acts as a charge pump but it which direction is the charge and subsequent energy pumping on the external circuit (out cathode-> in anode, or out anode-> in cathode)? – Anonymous555 Jul 17 '14 at 4:49
• Using the convention of positive current (we track the "movement" of positive charges), the cathode typically acts as a source of current. Thus the positive (+) terminal on a battery is the cathode. It turns out it doesn't matter which way you define current, since using EE conventions, you either get a positive voltage multiplied by positive current, or a negative voltage multiplied by a negative current. It works out the same either way. – Hari Ganti Jul 17 '14 at 7:22
• hope this would happens at some point: xkcd.com/567 – Blup1980 Jul 17 '14 at 12:01

## 2 Answers

If you are only confused by the "test particle," then you can think of it similarly to a multimeter. With a multimeter, you can probe a circuit to determine a voltage at one part of a circuit relative to another. With a test particle (or test charge, as I got used to hearing), you place it at a point in space, and "observe" it's behavior to see how electric (or magnetic) fields are oriented.

Like charges repel each other, so if a test charge would tend to move in a certain direction in space, then either that direction contains a negative charge (assuming you use a positive test charge), or the opposing direction contains a positive charge.

The movement of a test charge will always oppose the energy gradient (in three dimensions, energy is a scalar field, so the spatial derivatives are your forces, since energy divided by length is force). Thus, a test charge will move in the direction that achieves it's lowest energy state.

In a vacuum (such as space), ionized particles can move freely. The test charge is usually assumed to be in a state such that it can move freely. This doesn't necessarily correlate to anything real, but is a hypothetical state so the fields can be analyzed easily. You are correct in that circuits don't involve the movement of atoms or positive charges, but rather electrons (due to d-block delocalization, but that's chemistry) move. The positive charges (protons) are held in a crystalline lattice, which is why they don't move. In a conductor, electrons can move freely, so they move in response to an applied electric (or changing magnetic) field.

In free space, however, a test charge (which is really an ion, or a proton, or a positron, or a myriad of other positively charged particles) is not constrained by the bonds that hold metal atoms in place, so it can move in response to an applied field. Specifically, interactions governed by photons cause particles to exchange energy, creating the field gradient mentioned before. Therefore, test charges in free space move similarly to how electrons move in a metal (or another conductor).

While this is a convention (positive charges just seemed to be more reasonable when a lot of this math was derived), you could physically create a positively charged particle and observe it's trajectory. You could even do this at home. You'd be using a Cloud Chamber and a Beta emitter to see them.

I hope this was helpful! Let me know if you need any more clarification.

• Ah that makes more sense. I assume Mr. Faraday experimented on more then solid conductors to reach his conclusions about electric fields and thus using a a positive charged particle was more prudent in a number of situations. – Anonymous555 Jul 17 '14 at 16:49
• The root of my question was originally in trying to create a timeline for the creation of an electric circuit. Such that, an electric field is created at the positive terminal (external circuit, i.e cathode), this electromagnetic wave travels around the circuit back to its source (to repeat again) attracting electrons and giving a slight net movement towards the cathode. I suppose my real question would be then, how is energy moving from the anode (the negative electron having been energized by the work it took to get back to the anode from the cathode, internal circuit) to the load so fast? – Anonymous555 Jul 17 '14 at 17:01
• The electric field generated in a conductor is much stronger than one generated elsewhere. Therefore, electrons throughout a conductor are influenced by that field. If you find the voltage along a wire, you are seeing the field strength (in the free energy per unit of charge) at a point (relative to a different point). Thus, an electron need not travel from the anode to the load to do work, since an electron in or near the load can do work, since it gained energy from the electric field. – Hari Ganti Jul 19 '14 at 6:40

There is no such thing as a positive particle. You have electrons which are negative particles that moves from cathode to anode. What you describe as positive particles is much more a model (or a convention) then a real physical stuff.

An by the way, electrons are not really moving, but more like drifting at a rather slow speed.

Edit:

1) No, I refer to the electrons outside the battery. Let's assume a lead battery, which is very simple (same concept applies to other chemistries). You have an electrolyte which is filled with ions. When an electron leaves the cathode of the battery toward your circuit (yes, in reverse direction to what one would expect), the battery's inner plate, which is metallic lead, falls apart in the electrolyte. Note here: falling apart is not the work I seek, but English is not my first language, so... Well, the cathode disintegrates in the electrolyte in a process of oxide-reduction. The ions in the electrolyte plays the role of "holes" as they are positively charged and moves to the other side to recombine with incoming electrons. When your cathode's surface gets too small, your battery is discharged. To recharge it, you force electrons the other way around to reconstruct the cathode. I'm no chemist, so here ends the chemistry part. It may not be exactly what happens at chemical level, but the point is electrons leaves cathode and reenters at anode.

2) The anode is positive and the cathode negative. In reality, the electrons goes the other way around (cathode to anode). This is due to a mistake long ago, where it was though that electrons were positive. They found out later that in fact electrons were negative and moving the other way, so it is a convention to see the electricity flowing from anode to cathode. In practice, we don't care, it doesn't change anything in circuit design.

3) The electrons oscillate, so they transfer energy along the circuit, but they are not moving incredibly fast. They effectively drift at a rate of a few mm/hour. That means that physical electron particle moves along your circuit at that speed which is called "electron drift speed". It is rather complex, but you can imagine that when electrons are pulled out of the cathode, they generate a kind of local negative charge on the cathode, so the electrons are pulled toward the anode. Since you have a lot of electrons to push there is a kind of inertia, causing a slow drift speed, but there is still an oscillation along the wire causing DC current.

• I assume when you say "cathode to anode" you are referring to the internal circuit (i.e the movement of electrons from cathode to anode inside the battery)? If this is a convention then would the energy not flow (in the actual physical sense) in a copper wire circuit from anode(negative) to cathode(positive) on the external circuit with the energy being entirely gone/transformed by the time it reaches the cathode (and subsequently being re-energized with the work it takes to get the electrons back to the anode)? – Anonymous555 Jul 17 '14 at 4:46
• I had also assumed that electrons were still traveling at there 'normal' incredibly fast speed but the net movement towards the positive source of ALL the electrons in the circuit is very slow (on the order of mm/hour due to the weak pulling electric field and electrons constant re-balancing), is this incorrect? – Anonymous555 Jul 17 '14 at 4:54
• Wait. I can't type fast enough :) – Mishyoshi Jul 17 '14 at 4:55
• @Anonymous555: each individual electron travels slowly because of collisions, etc. however, since each electron repels every other electron not through bumping onto each other but through electromagnetic interaction, the net movement is at the speed of light. – Evan Jul 17 '14 at 11:50
• @Mishyoshi: technically, there exist positively charged particles. They are called protons. inside the batteries positively charged ions move around and recombine with electrons that reach the positive terminal. However, you are correct in that they won't be found inside of conductive wires. – Evan Jul 17 '14 at 11:55