Question

Charge particle in constant magnetic field
A particle of mass m and charge q is entering a region of space with uniform magnetic field
B⃗ . The particle initial (entering) velocity ⃗v0
has both components parallel and
perpendicular to the magnetic field B⃗ .
a) Write the equation of motion (EOM) for the particle and its general solutions.
b) Use relevant octave script provided to solve and plot the position of the particle as a
function of time.
c) Describe the state of motion of the particle based on the plots in part b)

Answer 1

Answer

a) equation of motion can be written by using lorentz force as

$F=q(E+v\times B)$

$F=ma=m\frac{dx^2}{dt^2}$

Using above both equation

$m\frac{d^2x}{dt^2}=q(E+v\times B)$

By applying above conditions in question

Solution is found

$x=A+C e^{\frac{qB}{m}t}$

B) above solution

$x=A+C e^{\frac{qB}{m}t}$

Compare with y=mx+c

So this is straight line equation with intercept A.

c) the state of motion of the particle based on the plots is straight line.