Supposedly, the drawing in Figure 20.4a is intended to look like the tip of an arrow coming out of a page,
and the drawing in Figure 20.4b is intended to look like the tail of an arrow going into a page.^1 These
symbols can be used to describe other ideas, such as electric fields going into or out of the page, or
currents flowing into or out of the page, but they are most often used to describe magnetic fields.
Long, Straight, Current-Carrying Wires
Bar magnets aren’t the only things that create magnetic fields—current-carrying wires do also. Of course,
you can also create a magnetic field using a short, curvy, current-carrying wire, but the equations that
describe that situation are a little more complicated, so we’ll focus on long, straight, current-carrying
wires.
The magnetic field created by a long, straight, current-carrying wire loops around the wire in
concentric circles. The direction in which the magnetic field lines loop is determined by a right-hand rule.
(Incidentally, our versions of the right-hand rules may not be the same as what you’ve learned in
physics class. If you’re happy with the ones you already know, you should ignore our advice and just stick
with what works best for you.)
Right-hand rule: To find the direction of the B field produced by long, straight, current-carrying wires.
Pretend you are holding the wire with your right hand. Point your thumb in the direction of the
current. Your fingers wrap around your thumb the same way that the magnetic field wraps around the
wire.Here’s an example. A wire is directed perpendicular to the plane of this page (that is, it’s coming out
straight toward you). The current in this wire is flowing out of the page. What does the magnetic field
look like?
To solve this, we first pretend that we are grabbing the wire. If it helps, take your pencil and place it
on this page, with the eraser touching the page and the point of the pencil coming out toward you. This
pencil is like the wire. Now grab the pencil with your right hand. The current is coming out of the page, so
make sure that you have grabbed the pencil in such a way that your thumb is pointing away from the page.
If it looks like you’re giving someone a “thumbs-up sign,” then you’re doing this correctly. Finally, look at
how your fingers are wrapped around the pencil. From a bird’s-eye view, it should look like your fingers
are wrapping counterclockwise. So this tells us the answer to the problem, as shown in Figure 20.5 .
Figure 20.5 Magnetic field (dotted lines) generated by a long, straight, current-carrying wire
oriented perpendicular to the plane of the page.