phy magnetism Q. 高手help 20點

The numerical figures given in the photo are very unclear. I could only try my best to figure them out.

(a) Let u be the speed of the ions. By balancing electric and magnetic forces
(1.6x10^-19).(70/0.1) = (0.1x10^-3).(1.6x10^-19)u
u = 7 x 10^6 m/s

(b) The ions follow a spiral trajectory along the magnetic field lines with constant radius.

(c) Component of velocity along the magnetic field lines = (7x10^6)cos(30) m/s
= 6.062x10^6 m/s
Distance travelled = 10/cos(30) m = 11.55 m
Time taken = 11.55/6.062x10^6 s = 1.905x10^-6 s

(d) Resolve u obtained in (a) in direction along field lines and perpendicular to field lines.
Hence, velocity perpnedicular to field lines = (7x10^6)sin(30) m/s = 3.5 x 10^6 m/s
Therefore, (1.6x10^-19).(3.5x10^6).(2) = (8.4x10^-27)(3.5x10^6)^2/R
where R is the radius of the spiral
R =(8.4x10^-27).(3.5x10^6)/[(1.6x10^-19).(2)] m = 0.09188 m
Period of revolution = 2.pi.(0.09188)/3.5x10^6 s = 1.649x10^-7 s
Hence, no of revolutions
= 1.905x10^-6/1.649x10^-7 = 11.6
No. of completel revolutions = 11

太遠睇唔到
遺憾
sorry