Convert cylindrical coordinates to Cartesian

[nuclearsneke]

TL;DR Summary

TL;DR - is it possible to convert from cylindrical to cartesian if I have no angular coordinate?

Good day!

I am currently struggling with a very trivial question. During my studies, I operated with a parameter called "geometrical buckling" for neutrons and determined it in cylindrical coordinates. But thing is that we usually do not consider buckling's dependence on angle so its angular coordinate is zero. How can I convert my vector B(r, phi, z) to B(x,y,z)? I have only Br and Bz.

 

[anuttarasammyak]

Ungiven $B_\phi$ seems to me that you are treating a ring around z axis. For an example we may have equal possibility of angle $\phi$ where the buckling would take place. Does it make sense ?

 

[Office_Shredder]

https://en.m.wikipedia.org/wiki/Cylindrical_coordinate_system

Has the conversion between cylindrical and Cartesian coordinates.

In the case of $\phi=0$ this is even easier. How does your choice of z in cylindrical coordinates influence the Cartesian coordinates, and what does $\phi=0$ say about the Cartesian coordinates?

 

[nuclearsneke]

https://en.m.wikipedia.org/wiki/Cylindrical_coordinate_system

Has the conversion between cylindrical and Cartesian coordinates.

In the case of $\phi=0$ this is even easier. How does your choice of z in cylindrical coordinates influence the Cartesian coordinates, and what does $\phi=0$ say about the Cartesian coordinates?

I know about jacobians. If my B_phi is 0, then I can just put my B(Br,0,Bz) as B(Bx,0,Bz)?
I will only have neutron leakage in x-axis and in z axis. That's preem!

 

[berkeman]

That's preem!

Are you a bicycle racer?

 

[nuclearsneke]

Are you a bicycle racer?

Nope, I am but a merely fan of cyberpunk2077 and its slang :)

 

[anuttarasammyak]

If my B_phi is 0, then I can just put my B(Br,0,Bz) as B(Bx,0,Bz)?

Let me check my understanding that you would like to understand the coordinates transformation between $B_x(x,y,z), B_y(x,y,z), B_z(x,y,z)$ and $B_r(r,\phi,z),B_\phi(r,\phi,z), B_z(r,\phi,z)$ ?
Then if $B_\phi(r,\phi,z)=0$
$$B_r^2=B_x^2+B_y^2$$
$$B_x=B_r \cos \phi$$
$$B_y=B_r \sin \phi$$
$$B_z(r,\phi,z)=B_z(x,y,z)$$