# B Question about the polarity of a voltage (PHY 2 for engineers)

#### mhrob24

My problem is understanding how the polarity of a voltage makes sense. For example, In my textbook, its states that "batteries move negative charges from its negative terminal to its positive terminal. In terms of potential, the positive terminal is at a HIGHER voltage than the negative terminal". Now, reading that just doesn't make any sense to me, and ill now explain my rationale:

If batteries move negative charges from a NEGATIVE terminal, then considering how Coulomb's law works; this means that the field from the negative terminal will produce a REPULSION force onto the negative charge (like signs repel). In terms of potential energy of the negative charge, this means that the negative charges being repelled from the negative terminal are GAINING kinetic energy and LOSING potential energy (If I manually took a negative charge being repelled by the negative terminal and moved it TOWARD the negative terminal, its would GAIN potential energy).

So with this logic in mind, as the negative charges are repelled toward the positive terminal.....then the negative charge being moved by the battery has LOST potential energy as it moves from its negative terminal to its positive terminal. If voltage is the change of potential energy, how the hell is the voltage at the positive terminal HIGHER than the negative terminal if the negative charge underwent a NEGATIVE change in potential energy as it traveled from its negative terminal to its positive terminal?

That seems backwards to me but I'm not the brightest bulb in the box so maybe I'm overthinking this and confusing myself somewhere, but I have read that the topic of voltage is one that tends to be quite confusing.

Thanks in advance to anyone who helps!

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#### Dale

Mentor
If voltage is the change of potential energy, how the hell is the voltage at the positive terminal HIGHER than the negative terminal if the negative charge underwent a NEGATIVE change in potential energy as it traveled from its negative terminal to its positive terminal?
Voltage (V) is the change of potential, not the change of potential energy. The change of potential energy is the voltage times the charge (QV).

So going from the negative terminal to the positive terminal V is positive, and for a negative charge Q is negative so the change in potential energy QV is negative.

#### anorlunda

Mentor
Gold Member
"batteries move negative charges from its negative terminal to its positive terminal.
If it really says that, it's wrong. A battery can cause current to flow from the positive to the negative terminal through an external circuit. A positive current is opposite to the direction of the flow of electrons. Double check your book. Is it talking about charges inside the battery or charges in the external circuit? (If you want to know who to blame for that horrible sign convention, it was Benjamin Franklin. A millenium from now, people will still be confused by that.)

But to understand a battery well, takes more than charges. It takes a little chemistry. Try this article, and see if it helps.

Homework Helper
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We have encountered that problem a couple of times, and it is necessary to distinguish between an electric field that is part of an EMF,( oftentimes written as $E_{induced}$, but it can also be part of a chemical potential in a battery), and an electrostatic electric field. $\\$ For the EMF, the voltage at B, (calling point A as zero voltage), is $V_B=\int\limits_{A}^{B} E_{induced} \cdot dl$. $\\$ For the electrostatic electric field, $V_B=-\int\limits_{A}^{B} E_{electrostatic} \cdot dl$.

#### mhrob24

If it really says that, it's wrong. A battery can cause current to flow from the positive to the negative terminal through an external circuit. A positive current is opposite to the direction of the flow of electrons. Double check your book. Is it talking about charges inside the battery or charges in the external circuit? (If you want to know who to blame for that horrible sign convention, it was Benjamin Franklin. A millenium from now, people will still be confused by that.)

But to understand a battery well, takes more than charges. It takes a little chemistry. Try this article, and see if it helps.

You are correct. I did not accurately quote my textbook. This was the case of a CIRCUIT connected to a battery moving a NEGATIVE charge from its negative terminal to its positive terminal (the circuit was a headlamp). So, if I truly do understand this time, the voltage is the potential difference of a charge moved from A to B DIVIDED by the charge (V = change in U/Q) Hence, independent of the charge, aka only dependent on the DIFFERENCE.

So really, the polarity of the voltage is just a matter of where you choose your origin (start point) to be. So in the example of a battery moving a charge in a circuit from its negative terminal to its positive terminal, the potential DIFFERENCE is positive because we defined our origin (start point) to be the negative terminal. So as the negative charge moves to the positive terminal, there is a positive DIFFERENCE (like going from 0 to 10). The only way for the Voltage in this case to be NEGATIVE is if the flow of the negative charges from the negative to the positive terminal is reversed. This would mean that our negative charge would be moving closer toward our origin point (the negative terminal). So like, going from 0 to 3 instead of 0 to 10. There is LESS of a DIFFERENCE from 0 going to 3 than there is from 0 to 10, so that would be a NEGATIVE potential difference aka a negative voltage....?

"Question about the polarity of a voltage (PHY 2 for engineers)"

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