The trajectory of a singly ionized helium atom for two full

Question

1 DRIFTS

Show that 0 = E + v x B can be solved to give

v = (E x B)/ B²

Hint: Use vector identities for the triple cross product.

2 SINGLE PARTICLE MOTION

(a) Starting fromthe Lorentz equation of motion for a single particle,

ma = q(E + v x B),

and assuming that the only components of the fields are: (i) radial for the electric field, E = E_rr^ , and (ii) axial for the magnetic field, B = B_zˆz. Show that Eq. 2.1 can be recast as

where Ω_i = qB/m and θ = ArcTan(y/x).

(b) Use the following boundary conditions: x(0) = x_o, y(0) = 0, x(0) = 0, and y(0) = -vo = -E_r/B_z, where x_o = 0.15m, E_r = 14300 V/m, and B_z = 0.2 T. Plot, using the software of your choice (e.g. Mathematica, Matlab, etc.), the trajectory of a singly ionized helium atom for two full revolutions around the z-axis.

(c) Repeat part (b), but using a singly ionized argon atominstead.