A proton is located at (0,0,0) at t=0 and has a velocity (0,v,0), where v is positive. The space is subject to magnetic field (0,0,B) where B is positive. As always, use CGS! a) Draw a sketch of the closed-loop trajectory of the proton. b) Will the magnitude of proton’s velocity change as a function time? Why? Prove it. c) Calculate ?⃗ (?) -- the position of the proton as a function of time in Cartesian coordinates. The final solution should not depend on any new variable – only time, initial velocity v, mass of the proton m, proton charge +e, field B. d) Write out the atomistic current density of the proton. e) Calculate the time-averaged current I due to the motion of the proton. Add it to the sketch. f) Based on this current, what is the field (as always, direction and magnitude) in the center of proton’s trajectory. Do not solve the integral, just give and draw the solution.
A proton is located at (0,0,0) at t=0 and has a velocity (0,v,0), where v is positive. The space is subject to magnetic field (0,0,B) where B is positive. As always, use CGS!
a) Draw a sketch of the closed-loop trajectory of the proton.
b) Will the magnitude of proton’s velocity change as a function time? Why? Prove it.
c) Calculate ?⃗ (?) -- the position of the proton as a function of time in Cartesian coordinates. The final solution should not depend on any new variable – only time, initial velocity v, mass of the proton m, proton charge +e, field B.
d) Write out the atomistic current density of the proton.
e) Calculate the time-averaged current I due to the motion of the proton. Add it to the sketch.
f) Based on this current, what is the field (as always, direction and magnitude) in the center of proton’s trajectory. Do not solve the integral, just give and draw the solution.
Step by step
Solved in 3 steps with 2 images
