# Particle in magnetic field, determining speed

• Tekee
In summary, the problem involves a particle moving at a 32-degree angle above the x-axis in a magnetic field pointing upward. It asks whether the speed of the particle is increasing, decreasing, or constant, and the same for its x, y, and z component velocities. The magnetic force on the particle is always perpendicular to its velocity, meaning it cannot change its kinetic energy. To solve the problem, we must look at the directions of the velocity, field, and force and translate them into xyz coordinates. We must also keep in mind that the answers found will be instantaneous changes in velocity.

## Homework Statement

There is a magnetic field pointing upward (say along the y-axis) and a particle going 32-degrees above the x-axis (or 58-degrees to the magnetic field)

The problem asks if the speed of the particle is increasing, decreasing or constant. It also asks if the x, y, and z components for speed are increasing, decreasing, or constant.

## The Attempt at a Solution

I figured that the direction of the field is coming out of the page, but don't know what is happening to the different speeds. I'm guessing the x/y components and overall speed stay the same but the z speed increases because there is a force acting on it.

Not enough information is given to determine anything about the speed.

There is enough information to solve the problem.

You must, however, make several distinctions.

The first is between "Speed" and "Velocity."

Velocity is a vector quantity, it is the speed in a given direction, while the speed of an object, has no direction.

Mathematically you can look at the speed as the magnitude of the velocity vector. The speed is all that matters, for instance, when determining kinetic energy, since that does not take into account the direction the object is moving in, but only the magnitude of its velocity.

Once you've chewed that over, remember that the magnetic force ALWAYS acts perpendicular to the velocity of a charged particle. That means that it can perform no work on that object, and going by the work-energy theorem, that means that it cannot change its kinetic energy. What does that tell you about the effect of a magnetic field on the speed of an object?

Having made that distinction, we should now refocus our thoughts on the effect a magnetic field has on velocity. A constant magnetic field will always provide an acceleration perpendicular to the velocity (This we know by the definition of the cross product and the Lorentz Force: $$\vec F_{magnetic}=q(\vec v \times \vec B)$$)

This nudges us to look at the directions of the velocity, field and force, and then translate them into our xyz coordinates, rather than doing it the other way around. Try that and see where it leads you. :)

Keep in mind that whatever answers you find, are the -instantaneous- changes in velocity in your xyz coordinate system.

I made a mistake in transcribing the problem. The problem asks for the overall speed of the particle, but asks for the velocity of the xyz components.

Nonetheless, I'm still confused at how to determine whether or not the component velocities are changing at all.

Tekee said:
I made a mistake in transcribing the problem. The problem asks for the overall speed of the particle, but asks for the velocity of the xyz components.

Nonetheless, I'm still confused at how to determine whether or not the component velocities are changing at all.

Net force on the particle in the direction of one of the axes = a net change in velocity over time.

## 1) How does a particle's speed affect its movement in a magnetic field?

The speed of a particle has a direct impact on its trajectory in a magnetic field. The faster the particle is moving, the larger the radius of its circular path will be. This is because the force exerted by the magnetic field on the particle is dependent on its speed.

## 2) What is the formula for calculating the speed of a particle in a magnetic field?

The formula for determining the speed of a particle in a magnetic field is v = Bq/m, where v is the speed, B is the magnetic field strength, q is the charge of the particle, and m is the mass of the particle. This formula is known as the Lorentz force equation.

## 3) How does the direction of the magnetic field affect the speed of a particle?

The direction of the magnetic field has no effect on the speed of a particle. The speed is only affected by the strength of the magnetic field and the properties of the particle, such as its charge and mass. However, the direction of the magnetic field does determine the direction of the particle's circular motion.

## 4) Can the speed of a particle in a magnetic field be changed?

Yes, the speed of a particle in a magnetic field can be changed if the magnetic field strength or the properties of the particle are altered. For example, if the magnetic field strength is increased, the speed of the particle will also increase. Additionally, if the particle's charge or mass is changed, its speed in the magnetic field will also be affected.

## 5) How is the speed of a particle in a magnetic field measured?

The speed of a particle in a magnetic field can be measured using various techniques, such as particle accelerators or mass spectrometers. These devices use the principles of the Lorentz force equation to calculate the speed of particles in a magnetic field. Additionally, the speed can also be determined by observing the trajectory of the particle in the field and using mathematical calculations to find its speed.