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How Is Voltage Induced In A Coil Of Wire?

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When a coil of wire is placed in a magnetic field or between two poles of the magnet and we move the coil forth and back, a current is induced in it. Because of this current a voltage is induced. This voltage is called induced voltage and it is induced due to the change in magnetic flux of the coil. The voltage can also be generated by moving magnet back and forth. If we take a current carry wire, a magnetic field will be there due to flow of current. If we change the current of wire, magnetic flux will also change due to this, voltage is induced in the wire itself. This is known as self induction. http://www.ndted.org/EducationResources/CommunityCollege/EddyCurrents/Physics/selfinductance.htm - 21k - 21k
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I am also working on developing a deeper understanding of electromechanics. I am designing a hybrid bike drive system right now. Magnet has a magnetic field, which results from the spin of the ceramic or other material being polarized in a crystal structure, this effects the "space time" around it. Materials quantum spins are effected by the magnetic field based on the crystal structure of the material. Ferro magnetic properties only found in iron are related to the number of free electrons.
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Quick Answer:To obtain actual numbers for voltage with a wire moving through a magnetic field it is a cross product of velocity, field strength, resistance etc. For a simpler calculation use Voltage = vBL, velocity of wire (m/s), magnetic field strength (Tesla) and length(meters). This assumes a wire moving perpendicular to a uniform field. For engineering design, calculus is usually needed to get any sort of efficiency. Better Answer:I am also working on developing a deeper understanding of electromechanics. I am designing a hybrid bike drive system right now. A PM has a magnetic field, which results from the spin of the material being polarized in it's crystal structure, this effects the "space time" around it. Materials quantum spins are effected by the magnetic field based on the crystal structure of the material. Ferro magnetic properties only found in iron are related to the number of free electrons and how EM fields interact with it. Iron and other materials having  high magnetic permeability are made into special alloys and then laminated to reduce hysteresis (eddy currents) while allowing the intended magnetic field to be directed, enacting forces. These forces are best understood by looking at Gaussian Surfaces, and then specifying more specific cases. You can think of an atom as a number of electrons moving in  paths which are oriented randomly along a spherical surface at a very fast rate, effectively creating a static electric field. When electricity flows though a wire the B field is said to encircle the wire, forming rings that decrease in intensity with the square of  distance. When a wire is formed into a circle, and a static electric field (voltage) is placed at the ends, electrons flow through the wire. Since the Field lines encircle the wire, the circular coil of wire will form a net magnetic field line that resembles a donut, much like our earth's, north and south depending on direction of current flow. Now imagine if the wire is wrapped in into a Toroid (which is the next 3d integral of a coil). The field lines, being perpendicular to the surface of the wire now form a circle, where the north and south "poles' of the magnet do not exactly exist, instead there is a region inside the toroid with maximum magnetic flux.Now consider a permanent magnet (donut shaped B field) within the standard coil and the toroidal coil's magnetic fields. If current is running through the coil of wire, the system will create forces which tend to align the poles of the magnets (torque) and merge the areas of greatest magnetic flux - inside the permanent magnet or coil). In the case of the circular coil, the net forces will align the two magnets, and pull them together until their centers touch. With the toroidal magnet, the PM will be pulled toward the nearest surface and align tangentially to the circumference of the toroid. If the PM where inside, it would align and be pulled to the center (levitated). Back to motors, a certain number of Amp-turns creates a certain amount of magnetic flux, and the efficiency is related to voltage, hysteresis, permeability, back emf, and lots of other stuff. As in the other example, a PM is experiencing an aligning torque and a force to increase the maximum flux in the system (solenoid force equation). On the stator of a 3 phase for example, There is a magnetic flux loop that allows the 3 phases to store energy in the magnetic field. 
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Holly North answered

A coil of wire inculed with voltage. This voltage is called induced voltage and it is induced due to the change in magnetic flux of the coil. If we take a current carry wire, a magnetic field will be there due to flow of current. If we change the current of wire, magnetic flux will also change due to this, voltage is induced in the wire itself. This is known as self induction.

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