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If the magnetic field is constant, the magnetic flux passing through a surface of vector area S is = = , where B is the magnitude of the magnetic field (the magnetic flux density) having the unit of Wb/m 2 , S is the area of the surface, and θ is the angle between the magnetic field lines and the normal (perpendicular) to S.
This situation is analyzed in the article, in which, when writing the integral equations of the electromagnetic field in a four-dimensional covariant form, in the Faraday’s law the total time derivative of the magnetic flux through the circuit appears instead of the partial time derivative. [36]
This is an eddy current. Similarly, the part of the sheet moving away from the edge of the magnet (the right side) experiences a decrease in magnetic flux density <, inducing a second eddy current, this time in a clockwise direction.
In this experiment, a static magnetic field runs through a long magnetic wire (e.g., an iron wire magnetized longitudinally). Outside of this wire the magnetic induction is zero, in contrast to the vector potential, which essentially depends on the magnetic flux through the cross-section of the wire and does not vanish outside.
(This definition of magnetic flux is why B is often referred to as magnetic flux density.) [35]: 210 The negative sign represents the fact that any current generated by a changing magnetic field in a coil produces a magnetic field that opposes the change in the magnetic field that induced it.
But when the small coil is moved in or out of the large coil (B), the magnetic flux through the large coil changes, inducing a current which is detected by the galvanometer (G). [1] A diagram of Faraday's iron ring apparatus. Change in the magnetic flux of the left coil induces a current in the right coil. [2]
The paradox appears a bit different from the lines of flux viewpoint: in Faraday's model of electromagnetic induction, a magnetic field consisted of imaginary lines of magnetic flux, similar to the lines that appear when iron filings are sprinkled on paper and held near a magnet. The EMF is proposed to be proportional to the rate of cutting ...
It determines the magnetic field associated with a given current, or the current associated with a given magnetic field. The original circuital law only applies to a magnetostatic situation, to continuous steady currents flowing in a closed circuit. For systems with electric fields that change over time, the original law (as given in this ...