Long, Straight, Current-Carrying Wires for AP Physics B & C

Practice problems for these concepts can be found at:

Magnetism Practice Problems for AP Physics B & C

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.)

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 birds-eye view, it should look like your fingers are wrapping counterclockwise. So this tells us the answer to the problem, as shown in Figure 22.5.

Here's another example. What does the magnetic field look like around a wire in the plane of the page with current directed upward?

We won't walk you through this one; just use the right-hand rule, and you'll be fine. The answer is shown in Figure 22.6.

The formula that describes the magnitude of the magnetic field created by a long, straight, current-carrying wire is the following:

In this formula, B is the magnitude of the magnetic field, μ₀ is a constant called the "permeability of free space" (μ₀ = 4π × 10^–7 T·m/A), I is the current flowing in the wire, and r is the distance from the wire.

Practice problems for these concepts can be found at:

Magnetism Practice Problems for AP Physics B & C