


The Magnetic Field Due to a Current
So far we have discussed the effect a magnetic field has
on a moving charge, but we have not discussed the reverse: the fact
that a moving charge, or current, can generate a magnetic field.
There’s no time like the present, so let’s get to it.
The magnetic field created by a single moving charge is
actually quite complicated, and is not covered by SAT II Physics.
However, the magnetic field created by a long straight wire carrying
a current, I, is relatively simple,
and is fair game for SAT II Physics. The magnetic field strength
is given by:
The constant is called the permeability
of free space, and in a vacuum it has a value of about N/A^{2}.
For SAT II Physics, it’s not important to memorize this
equation exactly. It’s more important to note that the strength
of the magnetic field is proportional to the strength of the current
and is weaker the farther it is from the wire.
The direction of the magnetic field lines are determined
by an alternate version of the righthand rule: if you held the
wire with your thumb pointing in the direction of the current, the
magnetic field would make a circular path around the wire, in the
direction that your fingers curl.
Example

Consider the magnetic field created by the bottom wire
as it affects the top wire. According to the righthand rule, the
magnetic field will point out of the page, and will have a strength
of B = (I)/(2πr).
The force exerted by the bottom wire on the top wire is F
= IlB.
If we substitute in for B the equation
we derived above, we find the force per unit length is:
Using the righthand rule once more, we find that the
force pulls the top wire down toward the bottom wire.
We can apply the same equations to find that the top wire
pulls the bottom wire up. In other words, the two wires generate
magnetic fields that pull one another toward each other. Interestingly,
the fact that each wire exerts an opposite force on the other is
further evidence of Newton’s Third Law.
