Particle in magnetic field, determining speed

[Tekee]

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.

Homework Equations

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.

 

[Delphi51]

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

 

[RoyalCat]

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.

 

[Tekee]

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.

 

[RoyalCat]

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.