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How did physicists come up with a standard for measuring charge? How an electrical measurement of charge was made?

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You can of course find this on wiki...or many other places.

Today, charge is related to the elementary charge e

The SI unit of charge, the coulomb, "is the quantity of electricity carried in 1 second by a current of 1 ampere A". Conversely, a current of one ampere is one coulomb C of charge going past a given point per second:

$1 A = 1 \frac{C}{s}$

The Ampere is defined by the elementary charge, see e.g. wiki for more detail than you probably want.

Practical measurement - if you have a capacitor of known strength, you can measure the charge on it with a voltmeter.

Hope that helps.

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