Unit of Charge
Quantization of Charge
The basic unit of charge, called the elementary charge, e, is the amount of charge carried by one electron.
Unit of Charge
The charge on a single electron is \({q}_{e} = \text{1.6} \times \text{10}^{-\text{19}}\text{ C}\). All other charges in the universe consist of an integer multiple of this charge. This is known as charge quantisation.
\(Q = n{q}_{e}\)
Charge is measured in units called coulombs (C). A coulomb of charge is a very large charge. In electrostatics we therefore often work with charge in micro-coulombs (\(\text{1}\) \(\text{μC}\)=\(\text{1} \times \text{10}^{-\text{6}}\) \(\text{C}\)) and nanocoulombs (\(\text{1}\) \(\text{nC}\)=\(\text{1} \times \text{10}^{-\text{9}}\) \(\text{C}\)).
Did You Know?
In 1909 Robert Millikan and Harvey Fletcher measured the charge on an electron. This experiment is now known as Millikan's oil drop experiment. Millikan and Fletcher sprayed oil droplets into the space between two charged plates and used what they knew about forces and in particular the electric force to determine the charge on an electron.
Example: Charge Quantisation
Question
An object has an excess charge of \(-\text{1.92} \times \text{10}^{-\text{17}}\) \(\text{C}\). How many excess electrons does it have?
Step 1: Analyse the problem and identify the principles
We are asked to determine a number of electrons based on a total charge. We know that charge is quantised and that electrons carry the base unit of charge which is \(-\text{1.6} \times \text{10}^{-\text{19}}\) \(\text{C}\).
Step 2: Apply the principle
As each electron carries the same charge the total charge must be made up of a certain number of electrons. To determine how many electrons we divide the total charge by the charge on a single electron:
\begin{align*} N & = \frac{-\text{1.92} \times \text{10}^{-\text{17}}}{-\text{1.6} \times \text{10}^{-\text{19}}} \\ & = 120 \text{ electrons} \end{align*}Example: Conducting Spheres and Movement of Charge
Question
I have \(\text{2}\) charged metal conducting spheres on insulating stands which are identical except for having different charge. Sphere A has a charge of \(\text{5}\) \(\text{nC}\) and sphere B has a charge of \(-\text{3}\) \(\text{nC}\). I then bring the spheres together so that they touch each other. Afterwards I move the two spheres apart so that they are no longer touching.
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What happens to the charge on the two spheres?
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What is the final charge on each sphere?
Step 1: Analyse the question
We have two identical negatively charged conducting spheres which are brought together to touch each other and then taken apart again. We need to explain what happens to the charge on each sphere and what the final charge on each sphere is after they are moved apart.
Step 2: Identify the principles involved
We know that the charge carriers in conductors are free to move around and that charge on a conductor spreads itself out on the surface of the conductor.
Step 3: Apply the principles
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When the two conducting spheres are brought together to touch, it is as though they become one single big conductor and the total charge of the two spheres spreads out across the whole surface of the touching spheres. When the spheres are moved apart again, each one is left with half of the total original charge.
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Before the spheres touch, the total charge is: \(-\text{5}\text{ nC} + (-\text{3}\text{ nC}) = -\text{8}\text{ nC}\). When they touch they share out the \(-\text{8}\) \(\text{nC}\) across their whole surface. When they are removed from each other, each is left with half of the original charge:
\[\frac{-\text{8}\text{ nC}}{2} = -\text{4}\text{ nC}\]on each sphere.
This lesson is part of:
Electric Charges and Fields