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The magnetic field lines follow the longitudinal path of the solenoid inside, so they must go in the opposite direction outside of the solenoid so that the lines can form loops. However, the volume outside the solenoid is much greater than the volume inside, so the density of magnetic field lines outside is greatly reduced.
Solenoid and B field with the flow through a surface S of base l Resuming the original definition of Maxwell on the potential vector, according to which is a vector that its circuitation along a closed curve is equal to the flow of B {\displaystyle \mathbf {B} } through the surface having the above curve as its edge, [ 3 ] i.e.
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.}
A magnetic field (sometimes called B-field [1]) is a physical field that describes the magnetic influence on moving electric charges, electric currents, [2]: ch1 [3] and magnetic materials. A moving charge in a magnetic field experiences a force perpendicular to its own velocity and to the magnetic field.
Lorentz force on a charged particle (of charge q) in motion (velocity v), used as the definition of the E field and B field. Here subscripts e and m are used to differ between electric and magnetic charges. The definitions for monopoles are of theoretical interest, although real magnetic dipoles can be described using pole strengths.
the magnetic field B changes (e.g. an alternating magnetic field, or moving a wire loop towards a bar magnet where the B field is stronger), the wire loop is deformed and the surface Σ changes, the orientation of the surface dA changes (e.g. spinning a wire loop into a fixed magnetic field), any combination of the above
E is the electric field, and; B is the magnetic field. The two equations for the EMF are, firstly, the work per unit charge done against the Lorentz force in moving a test charge around the (possibly moving) surface boundary ∂Σ and, secondly, as the change of magnetic flux through the open surface Σ.
The Aharonov–Bohm effect shows that the local E and B fields do not contain full information about the electromagnetic field, and the electromagnetic four-potential, (Φ, A), must be used instead. By Stokes' theorem , the magnitude of the Aharonov–Bohm effect can be calculated using the electromagnetic fields alone, or using the four ...