Reference no: EM13488211
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 = Err^ , and (ii) axial for the magnetic field, B = Bzˆz. Show that Eq. 2.1 can be recast as
where Ωi = qB/m and θ = ArcTan(y/x).
(b) Use the following boundary conditions: x(0) = xo, y(0) = 0, x(0) = 0, and y(0) = -vo = -Er/Bz, where xo = 0.15m, Er = 14300 V/m, and Bz = 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.