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
right-hand 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
Two parallel long straight wires carrying a current I stand a distance r apart. What force
does one wire exert on the other?Consider the magnetic field created by the bottom wire as it affects the top wire.
According to the right-hand 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 right-hand 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