We've just looked at a lot of examples
finding the direction of the magnetic
field at a point. However the direction is
only one component of the magnetic field,
strength is the other component. So let's
look at a few examples finding the
strength of a magnetic field due to a
current. Here we have a wire carrying a
current of five amps, and we want to find
the strength of the magnetic field three
meters away from the wire. When questions
ask for magnetic field, or indeed any
vector, it is always a good idea to give
direction as well as magnitude even if
it isn't asked for. This is because
vectors have both direction and
magnitude. Direction is what
distinguishes voters from scalars. Since
we need to give a direction, drawing a
diagram is important to help with
clarity. We are told that the current
runs from north to south, so let's label
a north, and draw a current from north to
south. Let's say this point is three
meters away from the current, then we
want to find the strength of the
magnetic field at this point. The
right-hand rule tells us that at this
point the magnetic field would point out
of the screen, and now all that's left is
to find the strength of a magnetic field.
We usually use the letter B to represent
the strength of the magnetic field, and
so B equals mu naught times I divided by
2 PI R. mu naught is just a constant
which we would look up or find on the
formula sheet. The current we are given,
and the distance we are also given. So
substituting in the numbers, we get this
expression: the PI's cancel and there's a
common factor of 2 as well, and we end up
with 3 times 10 to the negative 7
Tesls. Now, it's very hard to get an
intuition on the strength of the
magnetic field. So checking for
plausibility of number is hard. We could
do a units check though that would be
relatively simple in this case. The
constant mu naught has units Tesla
meters per amps. Current has units of
amps 2 and pi are both unitless,
and then we're dividing it by distance.
So meters the amps cancel so this
simplifies into Tesla meters per meter,
and then the meters cancel which gives
us Tesla's magnetic field is measured in
Tesla's so the units check out and don't
forget direction.
