Divergenceless example sentences

"Divergenceless" Example Sentences

1. The electromagnetic field must be divergenceless for Maxwell's equations to hold true.
2. A vector field can be called divergenceless if its divergence is zero.
3. A divergenceless flow will not produce a sink or source of fluid.
4. The irrotational part of a vector field is always divergenceless.
5. The magnetic field of a solenoid is divergenceless within the solenoid.
6. A Helmholtz decomposition can be used to split a vector field into a divergenceless and a curl-free part.
7. One way to ensure a fluid is divergenceless is to use a volume-preserving flow.
8. Divergenceless vector fields are also known as solenoidal fields.
9. The velocity field of an incompressible fluid must be divergenceless.
10. The fundamental lemma of vector calculus states that any curl-free and divergenceless vector field is equal to the gradient of a scalar field.
11. A bounded, divergenceless vector field on a closed surface encloses a net flux of zero.
12. A divergenceless vector field can be visualized as a flow that only expands or contracts, but never accumulates or vanishes.
13. The zeroth Maxwell equation states that the divergence of the electric field is proportional to the charge density, which implies that the electric field must be divergenceless in regions without charges.
14. The equilibrium condition for a plasma requires that the magnetic field be divergenceless.
15. The Green's function of the Laplacian operator in three dimensions is divergenceless and curl-free.
16. A magnetic field that is not divergenceless will either have sources or sinks, or both, in the form of magnetic charges.
17. The Navier-Stokes equations can be simplified by using a divergenceless velocity field.
18. A symmetry of a differential equation is a transformation that leaves the equation unchanged, such as a divergenceless flow.
19. A divergenceless field can be constructed by taking the curl of another vector field.
20. The curl of a divergenceless vector field is always a solenoidal field.
21. A two-dimensional divergenceless vector field can be represented as a scalar potential.
22. A vector field can be decomposed into its divergenceless and curl-free parts using the Helmholtz theorem.
23. The equation of continuity for a fluid implies that the velocity field must be divergenceless.
24. The Bianchi identities in general relativity relate the divergenceless parts of the Riemann tensor and its derivatives.
25. A divergenceless magnetic field can be generated by electrical currents in a solenoid or a torus.
26. The electric field of a point charge is divergenceless everywhere except at the charge location.
27. A divergenceless flow is useful in certain fluid-dynamic problems, such as the Kelvin-Helmholtz instability.
28. A stationary electromagnetic wave in vacuum is divergenceless in both the electric and magnetic fields.
29. The divergence operator applied to a divergenceless vector field produces zero.
30. The pressure gradient in an ideal gas is always a gradient of a divergenceless potential function.

Common Phases

1. The vector field is divergenceless;
2. Divergenceless flux is an important concept in physics;
3. The curl of a divergenceless vector field is always zero;
4. A divergenceless magnetic field does not have a source or sink;
5. The continuity equation requires a divergenceless flow of fluid;
6. Maxwell's equations require that the electric and magnetic fields be divergenceless;
7. Divergenceless operators play a key role in the theory of partial differential equations;
8. A divergenceless fluid flow can only conserve mass, not energy or momentum;
9. Divergenceless vector fields are often used to model ideal fluids and gases;
10. A divergenceless stress tensor is required for mechanical equilibrium.