Materials Science and Engineering/Equations/Magnetism

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Force of Charged Particle[edit | edit source]

When a charged particle moves through a magnetic field B, it feels a force F given by the cross product:

Force on Current-Carrying Wire[edit | edit source]

The formula for the total force is as follows:


F = Force, measured in newtons
I = current in wire, measured in amperes
B = magnetic field vector, measured in teslas
= vector cross product
L = a vector, whose magnitude is the length of wire (measured in metres), and whose direction is along the wire, aligned with the direction of conventional current flow.

Magnetic Field from Steady Current[edit | edit source]

The magnetic field generated by a steady current (a continual flow of electric charge, for example through a wire, which is constant in time and in which charge is neither building up nor depleting at any point), is described by the Biot-Savart law:

(in SI units), where

is the current,
is a vector, whose magnitude is the length of the differential element of the wire, and whose direction is the direction of conventional current,
is the differential contribution to the magnetic field resulting from this differential element of wire,
is the magnetic constant,
is the unit displacement vector from the wire element to the point at which the field is being computed, and
is the distance from the wire element to the point at which the field is being computed.

Magnetic Field Inside Coil - Empty Inductor[edit | edit source]


Energy per Unit Volume of Empty Inductor[edit | edit source]


Total Stored Energy in an Empty Inductor[edit | edit source]


Magnetic Field[edit | edit source]


Relative Permeability of a Material[edit | edit source]


Anisotropy Energy[edit | edit source]