Flux is integral along flat curve¶
The flux of a vector field exiting a boundary flat curve is defined as the line integral of the component of the field normal to the curve along the curve.
Conditions:
The normal to the curve is outward (see right-hand rule).
The vector field is continuously differentiable everywhere within the region of the surface.
The curve is closed and flat.
- Symbol:
H- Latex:
\(H\)
- Dimension:
any_dimension
- field¶
Vector field, i.e. a vector-valued function of the position vector.
- Symbol:
F- Latex:
\({\vec F}\)
- Dimension:
any_dimension
- unit_normal¶
Unit normal vector to the curve.
- Symbol:
n- Latex:
\({\vec n}\)
- Dimension:
any_dimension
- curve¶
Curve which is the boundary of the surface along which
fluxis calculated.- Symbol:
C- Latex:
\(C\)
- initial_parameter¶
Initial value of the curve parameter.
- Symbol:
u_1- Latex:
\(u_{1}\)
- Dimension:
dimensionless
- final_parameter¶
Final value of the curve parameter.
- Symbol:
u_2- Latex:
\(u_{2}\)
- Dimension:
dimensionless
- law¶
H = LineIntegral(dot(F, n) * norm(dr), C)- Latex:
- \[H = \int \limits_{C} \left( {\vec F}, {\vec n} \right) \left \Vert d \vec r \right \Vert\]