In the previous case study we had a
magnetic field of less than one microtesla
that's actually really small for a
magnetic field.
If we held a compass to the wire
you probably won't be able to
see a noticeable deflection.
So to get a bigger magnetic field
we can do a few things.
Looking at the equation mu naught and pi
are both constants, so we can't change
these variables, which means to change
the strength of the magnetic field we
need to shorten the distance of the wire or
increase the current. If we reduce the
distance, even to one centimeter, it won't
make a huge difference till you get to the
micrometer scale which is a bit hard for
everyday purposes. So that leaves us with
the other option to increase the current.
Only thick wires can conduct high currents.
A normal wire conducts only a
few amps before it will burn.
However creating strong magnetic fields
with thick wires like those you see on
telephone poles is super expensive and
hard to move around. So how we normally
solve this problem is to have lots of
thin wires. We have previously learned that
magnetic fields are vector fields, so
to find the overall magnetic field we add
up the individual magnetic fields if we
had a second wire right next to this
aqua one with a current going in the
same direction at the same strength the
overall magnetic field will be the sum
of the magnetic field due to both wires.
So let's call the magnetic field due to
the aqua wire B_A and the magnetic field
due to the brown wire B_B. Then the
overall magnetic field B_T will be a
sum of these two. We know how to find
 the magnetic field of a single current at
some distance r away,
B equals mu naught I divided by 2 pi r,
and since both have a current going in the same direction
the right hand rule will tell us that
the direction of the magnetic fields
would also be in the same direction.
Both wires have the same amount of current
running through them
and are the same distance away from our point.
Then B_T would equal
mu naught I divided by 2 pi r
plus mu naught I divided by 2 pi r, which is
the same thing
as doubling the magnetic field strength of one wire.
Now what if we had
more wires: ten, a hundred?
If all these wires have a current going in
the same direction, then they would all
generate the same magnetic field,
which will reinforce each other,
generating an even bigger overall magnetic field.
And if we apply the same analysis method
we get that the overall magnetic field is
just a number of wires times the
individual magnetic fields. So the
magnetic field due to multiple wires is
N mu naught I divided by 2 pi r, where N
is the number of current-carrying wires.
Increasing the number of wires is both
cheap and portable. Here's an example.
This is 600 turns of wire. Compare the
magnetic field around this to one wire.
Same current, same distance, but the
difference is no
