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 20.6 .
Figure 20.6 Magnetic field around a wire in the plane of the page with current directed upward.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, μ 0 is a constant called the “permeability of free
space” (μ 0 = 4π × 10−7 T·m/A), I is the current flowing in the wire, and r is the distance from the wire.
Moving Charged Particles
The whole point of defining a magnetic field is to determine the forces produced on an object by the field.
You are familiar with the forces produced by bar magnets—like poles repel, opposite poles attract. We
don’t have any formulas for the amount of force produced in this case, but that’s okay, because this kind of
force is irrelevant to the AP exam.
Instead, we must focus on the forces produced by magnetic fields on charged particles, including both
isolated charges and current-carrying wires. (After all, current is just the movement of positive charges.)
A magnetic field exerts a force on a charged particle if that particle is moving perpendicular to the
magnetic field. A magnetic field does not exert a force on a stationary charged particle, nor on a particle
that is moving parallel to the magnetic field.
The magnitude of the force exerted on the particle equals the charge on the particle, q , multiplied by the
velocity of the particle, v , multiplied by the magnitude of the magnetic field.
This equation is sometimes written as F = qvB (sin θ ). The θ refers to the angle formed between the
velocity vector of your particle and the direction of the magnetic field. So, if a particle moves in the same
direction as the magnetic field lines, θ = 0°, sin 0° = 0, and that particle experiences no magnetic force!
Nine times out of ten, you will not need to worry about this “sin θ ” term, because the angle will either
be zero or 90°. However, if a problem explicitly tells you that your particle is not traveling perpendicular