What's the voltage of a battery?

Question

The definition of voltage I'm familiar with is the amount of electric potential energy per unit charge at a location. My prof defined the voltage of a battery to be the amount of potential energy difference an unit charge would have at the positive terminal vs. the negative terminal.

But from what I remember from high school, the "terminals" aren't points, their rods of metal:

Since the voltage is defined at a point, not cylinders or rods what does the voltage of a battery mean? Also, how does the definition connect to the "pushing" power of a battery?

I took a look at Electrode Potential but it was a bit over my head.

I'm looking for an intuitive explanation, not one using rigorous chemistry concepts. Thanks!

Answer 1

Voltage is indeed something that is measured at a particular point, but that doesn't mean its a property of only one point and in fact every point will have some voltage. In particular you can have a series of points that map out an "equipotential" where the potential is equal all along these points. A terminal of a battery is an equipotential so no matter where an electron "is" it will have the same potential energy U = e V.

Intuitively this is just like potential energy due to gravity. The battery is like a mountain with a flat top and level plane at the base. Everywhere along the top the altitude is equal and a ball will have the same potential energy. Similarly everywhere along the level base of the mountain the ball will have the same potential energy.

Answer 2

An electrochemical cell which causes external electric current flow can be created using any two different metals since metals differ in their tendency to lose electrons. Zinc more readily loses electrons than copper, so placing zinc and copper metal in solutions of their salts can cause electrons to flow through an external wire which leads from the zinc to the copper.As a zinc atom provides the electrons, it becomes a positive ion and goes into aqueous solution, decreasing the mass of the zinc electrode. On the copper side, the two electrons received allow it to convert a copper ion from solution into an uncharged copper atom which deposits on the copper electrode, increasing its mass. Here the voltage of the battery means the potential difference between the two half cell, this is how the enode values are different . The bigger the difference in the enode value( its ability to lose or gain electrons) the bigger the voltage of the dry cell will be