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If I keep a compass with bar magnets all around it, all of equal strength and a compass in a center then what will happen? Will the compass start rotating?

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Viewing the compass as a dipole (it is not infinitesimal in size) if there is no field at the center the compass direction is not defined. It won't rotate-what will drive it? It will point in an arbitrary direction. In practice the field won't be zero-the magnets will not all be exactly the same (and if they were, the usual earth field would be sensed) so the direction will be well defined by the errors of the magnets.

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What will happen to compass with north all around it?

This happens at the North pole:

Here is an image of the magnetic lines at the poles. The simple compass follows the imaginary lines of the magnetic field and this is what it will do, follow the field line.

north pole

On the magnetic pole itself it will try to stand up if held horizontally, pointing towards the ground, making the needle unstable turning around since the south of the needle will be repelled and the north attracted by the field crossing the needle. If held vertically it will steadily point to the ground.

If left on the ground, it will be in an unstable position. It will stabilize in an arbitrary direction when the kinetic energy is dissipated, and will move if some is supplied ( vibrations) arbitrarily.

If I keep a compass with bar magnets all around it, all of equal strength and a compass in a center then what will happen? Will the compass start rotating?

The situation is similar, there will be field lines which from a distance will simulate one north pole. If the compass is held it will be rotating randomly, if left undisturbed the kinetic energy will dissipate and it will be in an unstable state pointing randomly.

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No force applied: no acceleration. It'll simply maintain whatever speed you spun it with (gradually slowing due to friction), or if its speed is 0, it'll point arbitrarily at whatever direction you set it to.

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