M10b-2.  Charged Particle in a Magnetic Field

As in M10a-2, ignore the gravitational force on the particle.

Do the following problems in the corresponding WebAssign assessment.

Problem A.  Orbiting particle

  1. Click here to open an IWP applet.   For this situation, the charged particle is in a magnetic field that points out of the screen. Run the animation without changing anything. Let it run even after it goes off the screen. It will come back. As the particle passes through (0,0), the direction of the net force on the particle is (+x,-x,+y,-y) <_>. We know this for two reasons. By Newton's <_> Law, the net force and <_> are in the same direction. The second reason is covered in the next item.

  2. Complete this: The magnitude of the particle's velocity does not change, because the only force acting on it, the <_> force, is always <_> to the velocity vector. For the same reason, the path of the object must be a <_>.

  3. You may have to try this a couple of times to get your timing right. Reset and run the applet. Change the magnetic field to negative. You should see the animation change even while it remains running. Now change the charge to positive to see another change. Tell what changed each time you switched the sign.

  4. Set the values for inputs given in WebAssign. Calculate the magnitude of the magnetic force acting on the particle.

  5. Which of the inputs given in question 4 have no effect on the magnetic force?

  6. Do some experimentation with this goal:  Determine how you must change (increase, decrease) each of the four inputs of charge, mass, initial velocity, and magnetic field in order to decrease the radius of the particle's motion.

  7. Here is the the most common net force problem involving magnetic force, and you need to be able to do it quickly whenever asked. Draw the force diagram for the particle, write the net force equation, and substitute and rearrange as needed in order to solve for the radius of the path, r, in terms of q, m, v, and B.  Your formula should be consistent with what you found in step 6.

  8. Reset the applet to its default values by closing and reopening it. Use your formula now to calculate what the magnetic field must be for the particle to move in a circle with the radius given in WebAssign. Check your result with the applet.

  9. In the previous problem, you used an equation for B. The units on the right-hand side of your equation should reduce to kg/Cs. These must also equal a tesla, which is a N/Am. Show that N/Am reduces to kg/Cs.

  10. Reset the applet to default values if necessary. Then change the particle to a proton by entering the charge and mass of that particle. Hopefully, you've learned by now to use the inside back cover of your text to look up useful information. Reset and run the animation. Describe the motion that you observe.

  11. While the proton appears to move at constant velocity, you know that can't be the case, since it's experiencing a magnetic force. You can easily explain the result to yourself by calculating the radius of the path.

Problem B.  The cyclotron condition

  1. Restore the applet to its original values. Change the magnetic field to the value given in WebAssign. Run the animation through one complete period of the motion. Record the period in the table in WebAssign to 3 significant figures. Repeat this for a velocity 10 times greater and another one-tenth as much.

Velocity
(m/s)		 Period
(s)
3.00E5 <_>
3.00E6 <_>
3.00E4 <_>

  1. Write a one sentence conclusion about the relationship between velocity and period.

  2. Now do the physics necessary to explain the relationship.  Start with your formula from step 6 above.  Use your textbook if necessary to help.

The result you found (or should have found) is called the cyclotron condition.  It's the theoretical basis for the operation of a cyclotron particle accelerator.  Your textbook doesn't describe how a cyclotron works, but you can find out more here.

Problem C.  Mass Spectrometer

  1. Click here to open another applet. Use this animation for this and the next two problems. Read the description accompanying the applet. What is the magnitude of the charge of each ion?

  2. Find the ratio of the radii of the two paths, rred/rblue, in terms of the ratio of the masses only. Show your work.

  3. Calculate the ratio of the masses (red to blue) to 3 significant figures.