Question

How is charge quantized?

Answer 1

Hint: Recall that all charges are defined in the context of an elementary charge that is usually taken to be the magnitude of charge possessed by an electron or proton. In such a case, determine the value of charge possessed by charged objects given that charge is quantized, i.e., they cannot possess continuous or arbitrary values of charge and will be discretely distributed in terms of the elementary charge. To this end, arrive at the nature of such charge distribution and determine the quantity that quantized charges in the first place.

Complete answer:
When we say that something is quantized, we mean that the values it entails are discrete and discontinuous. It basically means they are an integral multiple of some other value. By saying that charges are quantized, we are constraining the value of charge that it can possess to integral multiples of another quantity. This quantity is equivalent to the magnitude of charge possessed by an electron or a proton, and is called as the elementary charge, given as:
$e = 1.6 \times 10^{-19}\;C$
Thus, charge quantization implies that any charged particle can possess a charge equivalent to some integral number of $\;e$, i.e.,
$Q = ne$, where n=1, 2, 3, …
Thus, charge cannot take any arbitrary values but only values that are integral multiples of the fundamental charge.
The concept of quantization of charge was brought about by Millikan’s oil-drop experiment while attempting to measure the elementary electric charge. A small drop of oil was made to move in a known electric field at a rate that balanced the gravitational, viscous and electric forces. The gravitational and viscous forces were calculated from the size and velocity of the oil drop, enabling one to deduce the electric force. Since the electric force is nothing but the product of the electric charge and the known electric field, the charge of the oil drop was computed. By cumulative measurements of charges of many different oil drops it was seen that all charged particles possessed a charge equivalent to integer multiples of the elementary charge $\;e$
This is how we know that charge is quantized.

Note:
You may notice that particles like quarks do not possess charges equivalent to an integral number of elementary charges and are quantized into multiples of $\dfrac{1}{3}e$ instead. However, quarks are not isolated particles and exist in conjunction with other quarks. Such groupings will all have collective charges equivalent to integer multiples of$\;e$.
Also,$\;e$ is called as the elementary charge to imply that it is a basic and an indivisible unit of charge.