12/17/2023 0 Comments Magnetic flux equations![]() ![]() In the limit of a large magnetic Reynolds number, Alfvén's theorem requires that these surfaces of constant flux move with the fluid that they are embedded in. Consequently, the magnetic flux through these sides is zero, and the cross-sections along the tube's length have constant, equal magnetic flux. Flux tubes and field lines įurther information: Flux tube and Field line Surfaces S 1 and S 2 are cross sections of a magnetic flux tube the magnetic flux through S 1 is equal to the magnetic flux through S 2.Īlfvén's theorem is frequently expressed in terms of magnetic flux tubes and magnetic field lines.Ī magnetic flux tube is a tube- or cylinder-like region of space containing a magnetic field such that its sides are everywhere parallel to the field. ![]() Magnetic flux conservation implies that the magnetic flux through a surface moving with the bulk fluid velocity is constant, and magnetic field line conservation implies that, if two fluid elements are connected by a magnetic field line, they will always be. ![]() Motions of the two are constrained in that all bulk fluid motions perpendicular to the magnetic field result in matching perpendicular motion of the field at the same velocity and vice versa.įormally, the connection between the movement of the fluid and the movement of the magnetic field is detailed in two primary results, often referred to as magnetic flux conservation and magnetic field line conservation. Informally, Alfvén's theorem refers to the fundamental result in ideal magnetohydrodynamic theory that electrically conducting fluids and the magnetic fields within are constrained to move together in the limit of large magnetic Reynolds numbers ( R m)-such as when the fluid is a perfect conductor or when velocity and length scales are infinitely large. Later in life, Alfvén advised against the use of his own theorem. "On the Existence of Electromagnetic-Hydrodynamic Waves" interpreted the results of Alfvén's earlier paper "Existence of Electromagnetic-Hydrodynamic Waves" published in the journal Nature in 1942. Thus the matter of the liquid is "fastened" to the lines of force. In view of the infinite conductivity, every motion (perpendicular to the field) of the liquid in relation to the lines of force is forbidden because it would give infinite eddy currents. The concept of magnetic fields being frozen into fluids with infinite electrical conductivity was first proposed by Hannes Alfvén in a 1943 paper titled "On the Existence of Electromagnetic-Hydrodynamic Waves" published in the journal Arkiv för matematik, astronomi och fysik. This approximation breaks down in current sheets, where magnetic reconnection can occur. It is named after Hannes Alfvén, who put the idea forward in 1943.Īlfvén's theorem implies that the magnetic topology of a fluid in the limit of a large magnetic Reynolds number cannot change. The current induced in the coil creates another field, in the opposite direction of the bar magnet’s to oppose the increase.In ideal magnetohydrodynamics, Alfvén's theorem, or the frozen-in flux theorem, states that electrically conducting fluids and embedded magnetic fields are constrained to move together in the limit of large magnetic Reynolds numbers. Lenz’ Law: (a) When this bar magnet is thrust into the coil, the strength of the magnetic field increases in the coil. Faraday was aware of the direction, but Lenz stated it, so he is credited for its discovery. The direction (given by the minus sign) of the EMF is so important that it is called Lenz’ law after the Russian Heinrich Lenz (1804–1865), who, like Faraday and Henry, independently investigated aspects of induction. ![]() The minus means that the EMF creates a current I and magnetic field B that oppose the change in flux Δthis is known as Lenz’ law. The minus sign in Faraday’s law of induction is very important. The units for EMF are volts, as is usual. This relationship is known as Faraday’s law of induction. ![]()
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