Change independent variable in magnetic field line equations

[Jarvis323]

How can I convert this system of equations :

$$\frac{dz}{d\phi} = \frac{rB_z}{B_{\phi}},
\frac{dr}{d\phi} = \frac{rB_r}{B_{\phi}},
\frac{d\phi}{d\phi} = 1$$

to

$$\frac{dr}{dz},
\frac{d\phi}{dz},
\frac{dz}{dz}$$

 

[mfb]

You can use the chain rule.
Note: the third one is trivial.