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The Bjerrum length is the separation distance at which the potential electric energy of two elementary charges is equal to kB*T.

The electric potential energy of two elementary charges is inversely proportional to their separation distance.

Since kB*T is trivially proportional to temperature T, at a higher temperature you need to place two elementary charges closer to each other to get the electric potential energy equal to kB*T.

As the separation distance between those charges is defined as the Bjerrum length, the Bjerrum length is inversely proportional to temperature.

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