Charge Quantized: Explaining the Contradiction

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Charges are quantized, meaning they exist as integer multiples of the elementary charge (e), which aligns with the behavior of protons and electrons. Quarks, which possess fractional charges like +2/3e or -1/3e, do not contradict this principle because they combine in groups to form particles with integer charges. For example, a proton, made of quarks, has a total charge of +e. In macroscopic physics, only the charges of electrons and protons are relevant, as quarks do not exist freely to contribute to electric charge or current. Thus, the apparent contradiction is resolved by understanding the role of quarks in composite particles.
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When I first study the chapter Charge, I was told that charges are quantized, that is, you can't find a charge of like 6.2e or 1/3e.

But later, when I got into the quantum theory, I was told that there are quarks, which have charges like +2/3e or -1/3e.

Don't these two statements contradict?

How can we explain this contradiction?
 
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No, the two statements do not contradict one another. Any particle has a charge of an integer multiple of e. Particles, like the proton for example, are made up of a quarks, the sum of the charges of which will always equal an integer multiple of e-- in the case of a proton, +e.
 
I would like to add here that electric charges in the macroscopic world develop only due to exchange of electrons/protons. Though protons are made of quarks, these quarks never roam about freely to create any sort of charge or current in a body. So, we only consider the charge on an electron or a proton while studying electrostatics and electrodynamics, which ,as you know, always remains constant.

Mr V
 
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