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Magnetic field density, otherwise known as magnetic flux density, is essentially what the layman knows as a magnetic field - akin to a gravitational or electric field.
It can be more easily explained if one work backwards from the equation: <math>B=F/Il<math> where B is the magnitude of flux density in Teslas, F is the force experienced by a wire carrying current, I, and of length, l, all in SI units.
Demonstration of the left hand rule
So, one can see for a magnetic flux density to equal 1 Telsa, a force of 1 Newton must act on a wire of length 1 Metre carrying 1 Ampere of current.
1 Newton is a lot of force, and is not easily accomplished. To put it in perspective: the most powerful superconducting electromagnets in the world have flux densities of 'only' 20T.
This is true obviously for both electromagnets and natural magnets, but a magnetic field can only act on moving charge - hence the current, I, in the equation.
Indeed, the equation can be played around with to incorporate moving single charges, ie protons, electrons, and so on via <math>F=BQv<math> where Q is 1 Coulomb of charge and v is obviously the velocity of that charge.
The left hand rule can be used to determine the direction of motion/current/polarity from any two of those, as seen in the example.
de:Magnetische Flussdichte
nl:Magnetische fluxdichtheid
sl:gostota magnetnega polja
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