# Voltage in a circuit?

The voltage of the battery signifies the difference in voltage between the positive and negative terminal

What does this mean?

The definition of voltage difference I'm familiar with is the amount of potential energy charge one coloumb of charge would undergo from point A to point B.

At first I thought the quote was saying the voltage of the battery signifies the difference in potential energy one 1 C of charge would have if it were moved from the positive to the negative terminal.

But my interpretation of batteries is that they "push" electrons into the wire which push the electrons in front of them ahead which push the electrons in front of them ahead and so on.

How can I connect the two concepts of voltage being the difference in potential energy a charge would have if it moved from the positive to the negative terminal with the "pushing" power of a battery?

3. Now, if we connect the two terminals of a battery by a conducting wire, the wire now has its ends at different potentials, that is, there is a potential difference across the ends of the wire. This potential difference sets up an electric field within the wire from the positive to the negative($\vec E=-\nabla V$) terminal. This field is what does all the pushing. This field propels the electrons towards the positive terminal.