Consider a proton moving in the x-direction in a homogeneous magnetic field with a field axis in the z-direction

INSTRUCTIONS TO CANDIDATES

ANSWER ALL QUESTIONS

Mandatory Questions

Question 1

Consider a proton moving in the x-direction in a homogeneous magnetic field with a field axis in the z-direction. The proton has an energy of 1 MeV and the field strength is 3 T. Using an ordinary differential equation solver, follow the motion of this particle for 1 microsecond. Plot and describe the result.

Question 2

Launch the same proton (energy 1 MeV) in the same magnetic field (1 T, parallel to the z- axis), but this time the initial proton velocity has both an x- and a z-component. Follow the motion of this particle for 1 microsecond. Plot and describe the result.

Question 3

Change the magnetic field so that it is cylindrically symmetric around the z-axis. If R is the distance from the z-axis, in m, the magnitude of the magnetic field is 9T/R. The direction of the B-field at any point should be along a ring around z in the clockwise direction.

Launch a 1 MeV proton at R = 3 meters straight up (in the z direction) and plot the first microsecond. Describe the result.

Extended questions

Question 4

Repeat question 2, but make a 3d plot of your results. Depending on how you do that, you will have to include the line

from mpl_toolkits.mplot3d import Axes3D

in your import section.

Question 5

Repeat question 3, but make a 3d plot of your results.

Question 6

Evaluate the drift velocity in question 3.

Attachments:

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