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As the charge on electron is $$e^-=-1.6\times10^{-19}C$$ and charge on proton is $$p^+=+1.6\times10^{-19}C$$

Does this mean that the charge on electron is $3.2\times10^{-19}C$ less than that of charge on proton?

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No, The magnitude of charge on both the particles is same but opposite sign.

Actually the negative sign doesn't always mean "less", especially in physics. So, the charge on $e^-$ is not smaller than that of $p^+$.

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  • $\begingroup$ Comments are not for extended discussion; this conversation has been moved to chat. $\endgroup$ – ACuriousMind Apr 9 '17 at 12:50
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Negative doesn't necessarily mean less, especially in Physics. In most cases, negatives just represent the opposite direction. Or negatives represent something which has the opposite effect of the positive quantity. People often consider that negatives are less than 0. Yes, we write $-5<0$. But this 'less' is not the the same 'less' that we use in everyday world. It just represents a sense of order. $0$ represents nothing and anything can't possibly be below nothing.

Ask yourself this: Is 5 units North 'greater than' 3 units South. No, they're different things. But tracking South by a minus sign helps us in determining what is the end result or the effect. For example, go 5 units North, then 3 units South, you end up at $5-3=2units$ North. If the result is a negative number, then you end up at South. Even North could be represented by a '-' to keep track of sign.

But, if by greater, you mean 'more positive', then yes, the charge on a proton is $3.2\times10^{-19}$ greater than the charge on an electron only due to the sign convention (It could have easily been the other way around). Now, this 'greater' is not the same as 'greater' in everyday language. This 'greater' doesn't represent any 'improvement' in properties.

Another great example is work-done: You might ask: One can either do some work or no work. How can one do less than no work? This is not at all a 'mind-babbling' question because negative work is also some work. Here too, negatives are just keeping track of the direction. Just like going to South doesn't mean you've gone to a place less than nothing.

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The sign has nothing to do with the charge itself. It is just a convention. Just because we write an electron's charge as $-1.6\times10^{-19}$, it does not make the electron negative or its charge to be less than that of a proton.

We could have called charge on a proton to be $-1.6\times 10^{-19} C$ and the charge on an electron to be $1.6\times 10^{-19} C$. It does not make any difference in physics. Everything will continue to work the way it should.

Saying that a proton has $3.2\times 10^{-19}C$ of charge is not wrong. However, it is more useful to refer to the magnitudes while comparing charges. I would personally prefer to say negative $5\mu C$ is greater than positive $3\mu C$ as it conveys something useful.

However, when you are using those values in mathematical equations, you need to take their sign into account. In this case, $(p^+ - e^-)$ does give you $3.2\times10^{-19}C$.

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I think by saying the proton charge is higher than the electron charge you are thinking like on a temperature scale (degrees Celsius or Fahrenheit), where the temperature grows from negative to positive values. But charge does not work like that, it works more like speed, for example.

First, the zero represents something particular (no speed or neutral charge, which does not react to a non-zero electromagnetic field), and negative and positive are just set by convention.

Second, the sign is a pure convention and positive and negative values are perfectly symmetric. For speed, going forward or backward (positive or negative speed respectively) can be exchanged by changing the frame of reference. For charge, you can perfectly say that the proton has negative charge and the electron has positive charge and the physical laws will be the same. You will just have to change the sign of some physical constants, I assume.

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