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When I connect two identical disc magnets together, does the magnetic force double?

Yes, but only with sufficiently thin disc magnets.

"Sufficiently thin" means:

The height of the final magnet should not exceed the radius.

If you add more magnets, the force will increase, but only minimally. The magnet tends to approach a certain value that will never be exceeded regardless of the final height of the magnet.

Example:

Number of magnetsForce
1 x KT-10-01-N 0.5 kg
2 x KT-10-01-N 1.0 kg
3 x KT-10-01-N 1.5 kg
4 x KT-10-01-N 1.9 kg
5 x KT-10-01-N 2.1 kg
10 x KT-10-01-N 2.9 kg
50 x KT-10-01-N 3.8 kg
1000 x KT-10-01-N 3.9 kg
cs CZ sk SK