Biomedical Engineering Reference
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now). Experimental evidence shows the existence of an electrostatic force between electric
charges; the force between two X-type charges is always repulsive, as is the force between
two Y-type charges. The force between an X-type and a Y-type is always attractive. For
this reason, the early experimenters decided to classify charges as positive or negative,
because a positive quantity times a positive quantity gives a positive quantity, a negative
quantity times a negative quantity gives a positive quantity whilst a negative quantity times
a positive quantity gives a negative quantity. I am sure you know that the best known
fundamental particles responsible for these charges are electrons and protons, and you are
probably expecting me to tell you that the electrons are the negatively charged particles
whilst protons are positively charged. It is actually just a convention that we take: we could
just as well have called electrons positive.
Whilst on the subject, it is fascinating to note that the charge on the electron is exactly
equal and opposite of that on a proton. Atoms and molecules generally contain exactly
the same number of electrons and protons, and so the net charge on a molecule is almost
always zero. Ions certainly exist in solutions of electrolytes, but the number of Na + ions in
a solution of sodium chloride is exactly equal to the number of Cl ions and once again we
are rarely aware of any imbalance of charge.
A thunderstorm results when nature separates out positive and negative charges on a
macroscopic scale. It is thought that friction between moving masses of air and water
vapour detaches electrons from some molecules and attaches them to others. This results
in parts of clouds being left with an excess of charge, often with spectacular results. It was
investigations into such atmospheric phenomena that gave the first clues about the nature
of the electrostatic force.
We normally start any study of charges at rest ( electrostatics ) by considering the force
between two point charges, as shown in Figure 1.1. The term'point charge'is amathematical
abstraction; obviously electrons and protons have a finite size. Just bear with me for a few
pages, and accept that a point charge is one whose dimensions are small compared to the
distance between them. An electron is large if you happen to be a nearby electron, but can
normally be treated as a point charge if you happen to be a human being a metre away.
Q A
R A
R AB
Origin
R B
Q B
Figure 1.1 Point charges
The concept of a point charge may strike you as an odd one, but once we have established
the magnitude of the force between two such charges, we can deduce the force between
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