Jim has taught undergraduate engineering courses and has a master's degree in mechanical engineering.
A magnetic field exerts a force on a moving charged particle in ways that you might not expect. In this lesson, we're going to look at the direction of this force and the factors that affect its strength.
Force on a Moving Charge
When a charged particle travels through a magnetic field, it experiences a force unlike any other that we're familiar with in everyday life. To illustrate the point, envision yourself walking down the sidewalk, when all of a sudden, a strong gust of wind hits you from the side. Now imagine that instead of moving sideways, you shoot straight up to the sky. I know this sounds weird, but this is exactly what would happen if you were a charged particle and the wind was a magnetic field. In this lesson, we're going to talk about the factors that determine the strength and direction of this force.
The Importance of Relative Motion
A magnetic field cannot exert a force on a charged particle unless there is relative motion between the particle and the field. We can create a relative motion by either moving the particle through the field or by moving the field around the particle. It doesn't matter which, just as long as there is motion between them.
Now, just because there's relative motion between the particle and the field, it does not necessarily mean that the particle will experience a force. To help us visualize, imagine you're walking down the sidewalk again, but this time you're carrying a big sheet of plywood vertically at your side. If the wind came from a direction perpendicular to your path, which would be from your left or right side, you would experience a lot of force. However, if the wind came from a direction parallel to your path, which would be from your front or back side, you basically wouldn't feel any force at all. If the wind came from any direction in between, you'd experience a force that was less than if it came from the side, but more than if it came from the front or the back. Likewise, a charged particle traveling perpendicular to a magnetic field will experience the most force, while a particle traveling parallel to a magnetic field won't feel any force at all.
The force on a charged particle is always perpendicular to the magnetic field.
Our wind analogy can only go so far because, as mentioned before, the direction of the force on a charged particle would be vertical, and not side-to-side. To state it more accurately, the force is always perpendicular to both the magnetic field and the particle's direction of travel. That sounds really confusing, so let's do another thought experiment. If a charged particle was walking down the sidewalk and a magnetic field came at it from the side, the direction of the force would have to be either up or down because these are the only directions that are perpendicular to both the field and the electron's direction of travel. Now, if the field came down on the charged particle from above, the direction of the force would be either to the left or to the right, because again, these are the only directions that are perpendicular to both the field and the direction of travel.
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So, if the direction of force can be either left or right, how do we know which way the particle will go? Well, the answer to that question is dependent on several different factors. The first is whether the charged particle is positively charged or negatively charged. For example, if an electron traveled through a magnetic field that pushed it to the left, then a proton on the same path would be pushed to the right. The second factor is the direction of the magnetic field. If we reversed the direction of the field, our electron would now be pushed to the right, and the proton would be pushed to the left. The third factor is the direction in which the charged particle is traveling. If our electron is traveling through a magnetic field that is pushing it to the left, then reversing the electron's direction of travel will cause it to be pushed to the right.
Strength of Force
A stronger magnetic field exerts a stronger force on the particle.
The strength of the force on a charged particle is also dependent on a few different factors. The first is the magnitude of the charge on the particle. A particle with greater charge will experience a stronger force than a particle with a lesser charge. The second factor is the strength of the magnetic field. A stronger magnetic field exerts a stronger force on the particle than does a weaker field. The third factor is the speed of the particle relative to the field. The faster the particle moves in relation to the magnetic field, the stronger the force will be. The final factor is one we discussed before, which is direction. A particle will experience the greatest force when traveling perpendicular to the field.
When a charged particle moves relative to a magnetic field, it will experience a force, unless it is traveling parallel to the field. The sign of the charge, the direction of the magnetic field and the direction the particle is traveling will all affect the direction of the force experienced by the particle. However, the force is always in a direction that is perpendicular to both the magnetic field and the particle's direction of travel.
The strength of the force is directly affected by the magnitude of charge on the particle, the strength of the magnetic field and the speed of the particle through the field. Increasing any one of these factors will increase the force experienced by the particle. Direction also plays a role in the strength of the field. It is at a maximum when the particle moves perpendicular to the field and decreases as the direction of travel becomes more parallel. A particle traveling exactly parallel to a magnetic field will not experience any force at all.
Following this video lesson, you will have the ability to:
Recall what is needed for a magnetic field to be able to exert force on a charged particle
Explain why a charged particle traveling parallel to a magnetic field will not experience any force
Understand that the force is always perpendicular to both the magnetic field and the particle's direction
List the three factors that affect the direction of the magnetic force experienced by a charged particle
Describe the four factors that affect the strength of the magnetic force experienced by a charged particle
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