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# Magnetic field density

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. The SI unit of magnetic flux density is the tesla. 1 tesla = 1 weber (unit) / square metre.

It can be more easily explained if one work backwards from the equation: $B=\frac {F} {I l} \,$

where

B is the magnitude of flux density in teslas

F is the force in newtons experienced by a wire carrying

l metres in length

Demonstration of the left hand rule

So, one can see for a magnetic flux density to equal 1 tesla, 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 F = BQv

where

Q is 1 coulomb of charge

v is the velocity of that charge in metre per second

Fleming's left hand rule can be used to determine the direction of motion/current/polarity from any two of those, as seen in the example.

Other units of magnetic flux density are

## SI units

SI electromagnetism units

Name Symbol Dimensions Quantity
ampere (SI base unit) A C / s Current
coulomb C A · s Electric charge, Quantity of electricity
volt V J / C = kg m2 / (s2 C) Potential difference
ohm Ω V / A = kg m2 / (C2) Resistance, Impedance, Reactance
ohm &middot metre Ω &middot m kg m3 / (C2) Resistivity
farad F C / V = C2 s / (kg m2) Capacitance
farad per metre F / m C2 s / (kg m3) Permittivity
reciprocal farad F−1 kg m2 / (C2 s) Elastance
siemens S Ω−1 = C2 / (kg m2) Conductance, Admittance, Susceptance
siemens per metre S / m C2 / (kg m3) Conductivity
weber Wb V &middot s = kg m2 / (C s) Magnetic flux
tesla T Wb / m2 = kg / (C s) Magnetic flux density
ampere / metre A / m C / (s m) magnetic induction
ampere-turns / weber A / Wb C2 / (kg m2) Reluctance
henry H V &middot s / A = kg m2 s / (C2) Inductance
henry per metre H / m kg m s / (C2) Permeability
(dimensionless) - - Magnetic susceptibility

Last updated: 02-10-2005 21:17:48
Last updated: 05-03-2005 17:50:55