Magnetic field

:For other senses of this term, see magnetic field (disambiguation).

Formal definition

Like the electric field, the magnetic field can be defined by the force it produces. In SI units, this is:

Related Topics:
Electric field - Force - SI

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:

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mathbf{F} = q mathbf{v} imes mathbf{B}

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where

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:F is the force produced, measured in newtons

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: imes indicates a vector cross product

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: q is electric charge, measured in coulombs

Related Topics:
Electric charge - Coulombs

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: mathbf{v} is velocity of the electric charge q , measured in metres per second

Related Topics:
Velocity - Electric charge - Metres per second

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:B is magnetic flux density, measured in teslas

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This law is called the Lorentz force law.

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A simpler form of the force equation in a wire current loop is:

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Force = BLi = (Tesla)x(meter length of wire)x(ampere current of wire).

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A more complex explanation is that

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if the moving charge is part of a current in a wire, then an equivalent form of the law is

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:

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rac {dmathbf{F}} {d l} = mathbf{i} imes mathbf{B}

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In words, this equation says that the force per unit length of wire is the cross product of the current vector and the magnetic field. In the equation above, the current vector, mathbf{i}, is a vector with magnitude equal to the usual scalar current, i, and direction pointing along the wire that the current is flowing.

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The most compact and elegant mathematical statements describing how magnetic fields are produced makes use of vector calculus.

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In free space:

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: abla imes mathbf{B} = mu_0 mathbf{J} + mu_0 epsilon_0 rac { partial mathbf{E}} {partial t}

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: abla cdot mathbf{B} = 0

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where

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: abla imes is the curl operator

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: abla cdot is the divergence operator

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: mu_0 is permeability

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: mathbf{J} is current density

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: partial is the partial derivative

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:epsilon_0 is the free-space permittivity

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:mathbf{E} is the electric field

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: t is time

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The first equation is known as Ampère's law with James Clerk Maxwell's correction. The second term of this equation (Maxwell's correction) disappears in static or quasi-static systems. The second equation is a statement of the observed non-existence of magnetic monopoles. These are two of four Maxwell's equations; the notation is due to Oliver Heaviside.

Related Topics:
Ampère - James Clerk Maxwell - Magnetic monopole - Maxwell's equations - Oliver Heaviside

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