Update 3_drude_model_solutions.md - polish

src/3_drude_model_solutions.md

@@ -57,9 +57,9 @@ v_x'' = -\frac{e^2B_z^2}{m^2}v_x
 $$
 and the initial conditions, we find $v_x(t) = v_0 \cos(\omega_c t)$ with $\omega_c=eB_z/m$. From this we can derive $v_y(t)=v_0\sin(\omega_c t)$. 
 
-We can now calculate the particle position using $x(t)=x(0) + \int_0^t v_x(t')dt'$ (and similar for $y(t)$). We find a parametric expression for the position of the particle 
+We now calculate the particle position using $x(t)=x(0) + \int_0^t v_x(t')dt'$ (and similar for $y(t)$). From this we can find a relation between the $x$- and $y$-coordinates of the particle 
 $$
-(x(t) - x_0)^2 + (y(t) - y_0)^2 = \frac{v_0^2}{\omega_c^2}
+(x(t) - x_0)^2 + (y(t) - y_0)^2 = \frac{v_0^2}{\omega_c^2}.
 $$
 This equation describes a circular motion around the point $x_0=x(0), y_0=y(0)+v_0/\omega$, where the characteristic frequency $\omega_c$ is called the *cyclotron* frequency. Intuition: $\frac{mv^2}{r} = evB$ (centripetal force = Lorentz force due to magnetic field).