What would the magnetic field of two (practically identical) static cylindrical permanent magnets stuck together (called compound magnets) look like?

I am doing a science fair project on the Meissner effect and to achieve stability I had to put two cylindrical magnets next to each other (not on top, end to end) because I was levitating a superconductor above a magnet instead of a magnet above a superconductor. If I had been able to use just one magnet the field calculations seem rather straightforward (albeit complicated) but after considerable research, I found almost nothing about how to calculate the magnetic of two cylindrical magnets put end to end to each other forming what amounts to a magnet array. I found one article that described two cylindrical magnets stuck together in this manner as a compound magnet but they didn't do any calculations of the magnetic field.

I found this equation:

On Wikipedia on the article "Force Between Magnets" but these equations are for magnets on top of each other. I also found this website https://www.supermagnete.de/eng/faq/How-do-you-calculate-the-magnetic-flux-density, which details the different equations that can be used to calculate individual B fields (magnetic fields), but I am not sure how to apply the equations to multiple magnets.

A basic diagram of these magnets:

The magnets I used were the exact same size, this is just a basic diagram of how I arranged my magnets.

My question is if anyone would be able to help me to understand how to go about calculating the magnetic field of these two magnets? I am a high school senior and while I have an advanced math background these equations are very difficult for me to understand. My mom, who is a college math professor, is trying to help me through the mathematics but she doesn't understand the physics behind interacting magnetic fields.

• The equations you have are for force, not field, so they probably won't really help you. – Michael Seifert Feb 22 '18 at 16:56

Magnetic fields obey something called superposition. This means that if Magnet #1 creates a field $\vec{B}_1$ at a certain point in space without Magnet #2 present, and Magnet #2 creates a field $\vec{B}_2$ at that same point in space without Magnet #1 present, then the total magnetic field at that point in space when both magnets are present is simply $$\vec{B}_\text{total} = \vec{B}_1 + \vec{B}_2.$$ Note that this is a vector sum, i.e., you would need to decompose $\vec{B}_1$ and $\vec{B}_2$ into components to actually do this addition.