Batteries

What is the function of a battery? One may think that it is to store energy or create electricity, but the primary function of a battery is to maintain a constant potential difference between its terminals: the positive terminal at a higher potential, and the negative terminal at a lower potential. The difference between them is called the battery's emf \({\cal E}\), and is what you'll find printed on batteries you buy in the store: AA batteries have an emf of 1.5V, 9V batteries have an emf of 9V, car batteries have an emf of 12V, etc.

When the terminals of the battery are connected by a piece of metal, such as a wire, a competition ensues. The metal, being a conductor, wants to maintain a constant potential between its ends. The battery, on the other hand, wants the top of the wire to be at a higher potential than the bottom of the wire. The battery wins, in the short term, by continually pumping charge from one terminal to the other to maintain its desired potential difference. Once the positive charge reaches the positive terminal, it then flows "downhill" through the wire to the negative terminal. This continual flow of charge is called an electric current. The battery requires energy to pump charges uphill, which it gets from chemical processes that go on in the battery. When the chemicals have completely combined, the battery runs out of energy, and then the potential difference between the terminals returns to zero. The battery wins the battle, but the wire wins the war.

In this picture of a battery hooked up to a metal wire, what is the electric field at the star, inside the metal?
You may be tempted to say that the electric field is zero inside the wire. After all, it is a conductor, and we talked all about conductors in Section 8.4, right? But the electric field is zero inside a conductor only if it is in electrostatic equilibrium: that is, if the charges are motionless. The charges inside this wire are definitely moving, which means the wire is not in electrostatic equilibrium, which means that the electric field is not necessarily zero.

Instead, we can ask "why are the charges moving?" The battery sets up a potential difference, and positive charges are moving from higher potential to lower potential: that is, downhill. And in Section 7.6 we said that the electric field points downhill as well, so the electric field must be pointing in the direction the charges are moving. Or from another point of view, if we ask "what is pushing the charges through the wire?", clearly it must be an electric force. Positive charges feel a force in the same direction as the electric field. Thus the electric field at the star points downward.


There are other types of power sources besides batteries of course. In the lab, you will experiment with variable power supplies, which you can adjust to different voltages. Any discussion of "batteries" in future sections will apply to these power supplies as well. Batteries are traditionally represented with this symbol:

Wall sockets in the USA provide alternating current with an average voltage between 110V and 120V (depending on the electrical provider, the wiring in the house, and so forth). This behaves like the direct current of batteries in some ways, but differently than others. We will discuss alternating current in   TBD  .