# 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:

where

**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]

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

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

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## Magnetic Field[edit | edit source]

## Relative Permeability of a Material[edit | edit source]

## Anisotropy Energy[edit | edit source]

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