Flux density

Flow through a sample area

The flux density is a vector field which describes the amount of a physical quantity that flows through a sample surface per surface element . The total amount is called the flow , so it results: ${\displaystyle {\vec {F}}}$ ${\displaystyle \mathrm {d} {\vec {A}}}$ ${\displaystyle S}$ ${\displaystyle \Phi }$

${\displaystyle \Phi =\int _{S}{\vec {F}}\mathrm {\cdot } \mathrm {d} {\vec {A}}}$

In general:

${\displaystyle {\vec {F}}={\frac {\mathrm {d} \Phi }{\mathrm {d} A}}\cos(\theta ){\vec {e}}_{F}}$

where is the angle between and the normal of the surface element and the unit vector in the direction of . ${\displaystyle \theta =\arccos \left({\frac {{\vec {F}}\mathrm {d} {\vec {A}}}{|{\vec {F}}|\cdot |\mathrm {d} {\vec {A}}|}}\right)}$ ${\displaystyle {\vec {F}}}$ ${\displaystyle \mathrm {d} {\vec {A}}}$ ${\displaystyle \mathrm {d} {\vec {A}}}$ ${\displaystyle {\vec {e}}_{F}={\frac {\vec {F}}{F}}}$ ${\displaystyle F}$

If the surface is oriented perpendicular to the flow direction, the following applies:

${\displaystyle {\vec {F}}={\frac {\mathrm {d} \Phi }{\mathrm {d} A_{\perp }}}\cdot {\vec {e}}_{F}}$

In addition to flux density , the term fluence rate ("fluence rate") is also used in English .

Examples

• Electric flux density of the electric field
• Magnetic flux density of the magnetic field
• Momentum current density
• Electric current density

See also

• Fluence (particles per area)
• electrical current density , dielectric
• Radiant flux density ( irradiance ), luminous flux density ( illuminance )
• Particle flux density
• Neutron flux density