Let's take a quick aside and discuss
fields
Now mathematically a field is
just something that has a value for each
point of space.
What kind of value?
That's a kind of generic thing, the answer is any kind of value.
It can even have units and
different kinds of values for each point
in space we'll define different kinds of
fields. And you've met heaps of these. In
a simple weather report, we might see
four or five different kinds of fields.
The first thing we might see is a
temperature map,
so that tells us the temperature all
over the country and any given point on
this map is a particular color which
specifies a particular temperature so
for every point in space on this map we
have a temperature mathematically that's
called a temperature field.
Well they might show us the pressure so
when you're talking about the weather
it's really useful to know where the
high and low pressure areas are and so
we have high atmospheric pressure here
and they usually slap an H on it and
they have low pressure over here and
that's really important in a weather
report because where you got high and
low pressure areas it's going to have a
strong effect on winds it's gonna have a
strong effect on where rain clouds go
and things like. It's quite useful
to use this contour map to show the
pressure because you can really see
there where the hills are in the high
pressure and where the valley is for the
low pressure and what these contours are
that a contour is a line where the
pressure is the same and so the pressure
is the same all the way around there and
so it's higher as you go up so this is a
gradient as you go across the contour
lines you've got a gradient and so there
what the pressure going up and here
going into this low got the pressure
going down.
But all we're representing
here is for each point on this map, we
have a value for the pressure and so
mathematically this is an example of a
pressure field, so another really handy
thing to learn when you're watching the
weather is the wind and what you expect
the wind to be and what it is now and
the wind of course has both a strength
and a direction. So something has a
magnitude and a direction is a vector
and if you want to show that the wind is
different in different places you can
draw different vectors all over this map
and so what we have here of course is
just following the theme we have for
each point in space our velocity and so
this is an example of a velocity field.
So, these two here the temperature and
the pressure are just a single number at
each point in space so the temperature
is measured in Celsius or Fahrenheit or
Kelvin and the pressure is measured in
Pascal's or atmospheres and any physical
quantity in physics that's described by
a single number is called a scalar and
so these are scalar fields and the
velocity is a vector field because we've
got a vector each point in space.
We can think of lots of other examples of
these so the volume of sound coming over
speaker changes as you move around and
so intensity might be a good scalar field.
Density might be really important
one if you're a geologist you really
want to know where the dense rocks are
and where the oil is and so knowing the
density field might be really useful.
We've already met various vector
quantities that change as you move
around in space velocity of say wind
might be one another might be the
gravitational field. So, we've already met
the gravitational field and we know that
things will accelerate differently
whether they're close to or further away
from other masses and that's because
they're experiencing indifferent Falls
and if the force changes in space that
it must be a field.
Key warning here is
that if you say force field to a science
fiction enthusiast then they're going to
think you mean some kind of invisible
barrier created by something akin to
magic whereas if you say it to a physicist
they're going to think you
mean a force for each point in space and
so be very careful who you're talking to
particularly if you're talking to a
physicist who like science fiction in
which case you're just going to have to
be very careful to communicate. So the
idea of fields was actually introduced
by Isaac Newton when he was describing
gravity for the first time and the
concept was developed a lot more in the
study of electromagnetism.
Of course in this section we're going to be
talking about electric fields and
magnetic fields
