Uniform Magnetic Field's Effect on Moving Charges

[wolfpack11]

Homework Statement

Charges 1 and 3 in the figure below have the same mass and the same speed. Which has the greater magnitude of charge? What are the signs of the charges?

http://www.webassign.net/colfunphys1/21-p-001.gif

Homework Equations

F = |q|v*B*sin(θ)

The Attempt at a Solution

The x'es indicate that the direction of the magnetic field is into the screen. What are the arrows referring to? I think the solution has to do with what's perpendicular to the field, and the x-and y- components of these arrows. Can someone help interpret and explain? Thanks!

 

[berkeman]

Homework Statement

Charges 1 and 3 in the figure below have the same mass and the same speed. Which has the greater magnitude of charge? What are the signs of the charges?

http://www.webassign.net/colfunphys1/21-p-001.gif

Homework Equations

F = |q|v*B*sin(θ)

The Attempt at a Solution

The x'es indicate that the direction of the magnetic field is into the screen. What are the arrows referring to? I think the solution has to do with what's perpendicular to the field, and the x-and y- components of these arrows. Can someone help interpret and explain? Thanks!

The arrows refer to the paths taken by the 3 particles. From the direction they bend, and from their radii, you can infer things about their mass and charge...

 

[HallsofIvy]

You titled this "Uniform Magnetic Field ..." but it looks to me like the whole point of this problem is that the field is NOT uniform- and that's why particles with the same charge and mass have different trajectories.

 

[nasu]

You titled this "Uniform Magnetic Field ..." but it looks to me like the whole point of this problem is that the field is NOT uniform- and that's why particles with the same charge and mass have different trajectories.

They don't have the same charge.

 

[xienwolf]

The arrows, as Berkeman said, show you the path that the charges move along as time progresses.

So, what causes an object to curve? Changing direction means a change in velocity, so an acceleration. You cannot accelerate without a force being applied, so where is the force in this case?

What can you tell us about Charge 2, since it did NOT curve?

Charge 1 curved to the left, and charge 3 curved to the right, the field is down. So from this you should be able to state which is positive and which is negative.

The last element is in which curve is a portion of a smaller radius circle. That would mean a stronger force applied. How do you get a stronger force applied from the same magnetic field?

 

[wolfpack11]

Thanks for clearing it up a bit, xienwwolf. I don't know how to answer your questions though.

I'm still confused on how you can tell which charge is positive and which is negative based on their directions of motion and the field direction. Can someone explain the underlying concept/reason for this? My whack at an explanation is that the field/field lines are defined as moving from positive to negative (or vice-versa, from negative to positive), which would mean that positive and negative charges tend to move towards their opposite poles.

And why does a smaller radius of motion mean a stronger force applied? It seems that the magnetic force would be in the positive y- direction because it would then be perpendicular to both the field and the motion/velocity/displacement. From the equation though, it's evident that the uniform field produces stronger forces on larger charges.

Thanks a million!

 

[xienwolf]

Look in your book for something called the "right hand rule" and see if that clears up your confusion about direction/charge.

The field lines are defined by the "X" symbols. That means the field lines point into the screen/paper. Field lines are drawn from North to South outside of a magnet, so that means the North Pole is where your eyes are, and the South Pole is on the other side of the screen/paper.

You are correct in saying that the force should be perpendicular to both the field and motion. But you are incorrect in saying that the force would always be in one direction.

Right where the charges are drawn (initial velocity), in which direction are they moving (instantaneous velocity)? At the end of the arrows, in which direction are they now moving?

As for questions you do not know how to answer: The best approach is to type out what your thoughts are when you attempt to answer the questions. That allows us to see your reasoning and fill in the gaps, or help you make a small connection to continue moving along the line of reasoning. Each of my questions are designed to help you pick up a vital piece of information for answering the problem. So any question you cannot answer indicates a reason for why you cannot finish the original problem.