The magnetic field for magnets comes out
of the north pole and goes into the
south pole. A current also generates a
magnetic field as we've previously
discussed, but there is no north or south
pole in this case. So how do we find the
direction of the circular magnetic field
around the current? Oersted discovered the
magnetic field around the current, but it
was Ampere that described the direction
of the magnetic field. He said that if
one were to imagine a little mannequin
to swim in the direction of the current,
and to face the needles. Then the north
pole of the needle would be the
direction of the left arm and the south
pole that of the right arm. This
description is slightly hard to follow
so these days we use the "right hand rule"
to identify the direction. The right hand
rule is called the right hand rule
because you use your right hand. So you
put your thumb in the direction of the
current, and you curl your fingers around
the current. The direction which your
fingers curl tells you the direction of
the magnetic field. So let's say you had
a current carrying wire and in it there
is a current going towards the left. So
you curl your fingers around the wire
and the direction what you think this
curl will show you the magnetic field. So
in this case, on top of the wire, the
magnetic field points out of the screen
towards you. In front of the wire, the
magnetic field points down. Underneath
the wire, the magnetic field points
towards me. And behind the wire, the
magnetic field points up. Because
magnetic fields have direction, if we
look at a current going up, the magnetic
field goes into the screen on the right
hand side of the wire, and comes out of
the screen on the left hand side of the
wire. How we draw this is by using
crosses to indicate that the magnetic
field goes into the screen. This can be
thought of as an arrow going away from
you. And dots indicate a magnetic field
coming out of the screen, and are going
towards you. Now that we have the
direction of the magnetic field at a
point, we can also find the strength of
the magnetic field due to a current at
that point. Just like electric fields, the
strength of the magnetic field increases
the closer you are to the current and
decreases further away: the stronger the
current the
stronger the field. So applying Ampere's law,
we get this formula describing the
magnetic field strength:
B = μ₀ × I divided by 2πr where B
is a strength of the magnetic field in
teslas, μ₀ is a constant. It is 4π × 10⁻⁷,
also known as the permeability of free
space and measured in Tm/A.
I is the strength of the current,
measured in A, and r is the
perpendicular distance from the current,
measured in m. The formula shows the
strength of the magnetic field
increasing as the strength of the
current increases. This fits with our
expectations from the experiment. The
magnetic field strength also increases
as distance from current decreases, which
also fits with the experiment so this
formula behaves the way we want it to.
