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Calculating the force between two magnets is very difficult in detail. If the magnets are free to rotate, the force is given by the magnetic moment of magnet #1 times the rate of change of the field of magnet #2. Reversing the labels on the magnets has no effect on the force. At distances larger than 2 or 3 times the size of the magnet, the field varies as the inverse cube of the distance. Hence the force varies as the inverse fourth power. This is why magnets do not exert much force until they are close together. A factor of two increase in the separtation lowers the force by a factor of 16! Calculating the force when the magnets are close together or when they are not free to rotate requires a very comlicated computer program.

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