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An example of a solenoidal vector field, (,) = (,) In vector calculus a solenoidal vector field (also known as an incompressible vector field , a divergence-free vector field , or a transverse vector field ) is a vector field v with divergence zero at all points in the field: ∇ ⋅ v = 0. {\displaystyle \nabla \cdot \mathbf {v} =0.}
This is a derivation of the magnetic flux density around a solenoid that is long enough so that fringe effects can be ignored. In Figure 1, we immediately know that the flux density vector points in the positive z direction inside the solenoid, and in the negative z direction outside the solenoid.
In physics, the electric displacement field (denoted by D), also called electric flux density is a vector field that appears in Maxwell's equations. It accounts for the electromagnetic effects of polarization and that of an electric field , combining the two in an auxiliary field .
In electromagnetism, electric flux is the total electric field that crosses a given surface. [1] The electric flux through a closed surface is equal to the total charge contained within that surface. The electric field E can exert a force on an electric charge at any point in space. The electric field is the gradient of the electric potential.
A solenoid The longitudinal cross section of a solenoid with a constant electrical current running through it. The magnetic field lines are indicated, with their direction shown by arrows. The magnetic flux corresponds to the 'density of field lines'. The magnetic flux is thus densest in the middle of the solenoid, and weakest outside of it.
where this time is the charge density, is the current density vector, and is the current source-sink term. The current source and current sinks are where the current density emerges σ > 0 {\displaystyle \sigma >0} or vanishes σ < 0 {\displaystyle \sigma <0} , respectively (for example, the source and sink can represent the two poles of an ...
where is the magnetic flux density, or magnetic flux per unit area at a given point in space. The simplest example of such a system is a single circular coil of conductive wire immersed in a magnetic field, in which case the flux linkage is simply the flux passing through the loop.
Aharonov–Bohm effect apparatus showing barrier, X; slots S 1 and S 2; electron paths e 1 and e 2; magnetic whisker, W; screen, P; interference pattern, I; magnetic flux density, B (pointing out of figure); and magnetic vector potential, A. B is essentially nil outside the whisker. In some experiments, the whisker is replaced by a solenoid.