Why is the electric charge of a body quantised?

1 Answer
Oct 3, 2014

When scientists say that some sort of property is quantized (charge, energy, etc.), they mean that the property can only have discrete values. Discrete is the opposite of continuous, and it is important to have an example for both to highlight the distinction.

To think of a continuous property, consider driving from home to school, and suppose your school is exactly one kilometre away. On your drive, you could be anywhere between your house and the school. You could be half a kilometre away (0.5 km), one third of a kilometre away (0.33 km), or an even more precise distance such as 0.4773822 km way. Since you could hypothetically be anywhere along the entire 1 km spectrum, distance can be thought of as a continuous property.

For a discrete property, consider climbing up a flight of stairs. If there are a total of 10 stairs, it is possible to be on stair 1, or 2, or 3, and so on. But it's not possible to be on stair number two and a half, stair number 6.8743. In other words, the possible value for stair numbers is discrete, or quantized.

Now we will look at this distinction in the context of electric charge. At the most elementary level, charge is controlled by the combined total number of protons and electrons. If an object has an excess of electrons relative to protons, it will be negatively charged. The question becomes, "how much negative charge"?

Charge is measured in units of Coulombs, C. Each proton has a charge of #+1.602*10^-19 C# and each electron has a charge of #-1.602*10^-19 C#, which we can denote as #+e# or #-e#. Just to be clear,

#e=1.602*10^-19 C#

So any object, or body, with a net charge (i.e. excess of either protons or electrons) must have a value of plus or minus #e#, or #2e#, or #3e#, and so on (in technical terms, an integer multiple of #e#). However, it would be impossible for an object to have a charge of #+1.3e# or #-4.57e#.

For further information, take a look at the following resource: http://en.wikipedia.org/wiki/Elementary_charge#Quantization.