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Electromagnetism � The magnetic field is described by the vectorial field B [N / A m = Tesla = T] Electric currents generates magnetic fields. The magnetic field induced by an electric current flowing through an straight wire of infinite length is µ·i B= 2πd B magnetic field induced by the wire (are concentrical circles centred in the wire and orthogonal to it). The direction � is given by the right hand rule. d distance between the of B wire and the point on which the magnetic field is calculated. Magnetic field in the centre of a wire loop nµ · i B= 2R B magnetic field generated by the current i flowing through a wire loop with n windings of radius R, calculated in the centre of the wire loop. R) Magnetic field in the centre of a rectilinear solenoid (l � nµ · i B= l B magnetic field generated by the current i flowing through the solenoid of length l. Ferromagnetism A ferromagnetic material is composed by microscopic magnets (<<1 mm) generated by the motion of electrons in the atomic orbitals which act as tiny wire loops As a consequence of a sufficiently strong magnetic field the tiny magnetic areas can be orientated conformally, amplifying of several order of magnitudes the resulting magnetic field. If the external magnetic field is sufficiently strong the small magnetic areas can be orientated conformally in a permanent way. This generated a magnet. Electric motor A simple DC (Direct Current) motor. As the current flows in the loops, a magnetic field is generated around the rotor. The left side of the rotor is repulsed by the left magnet while the right side is attracted by the right magnet. This generate a torsion. The rotor continue to rotate by inertia As the rotor is horizontal a commutator inverts the direction of the current through the wire loops, modifying the polarity of the induced magnetic field. The process is thus again in the initial state and the cycles starts over. The AC motor works without commutator since the inversion of polarity of the magnet is given by the inversion on the current direction Magnetic force (Lorentz’s force) |F | = q · v · B · sin θ F Force generated by a magnetic field on a charged particle (e.g. electrons) in motion. q, �v = charge and velocity of the � magnetic field. Lorenz’s Force F has direction particle. B � perpendicular to the plane containing the vectors �v and B, and is direction is given by the right hand rule. Force applied on a segment of rectilinear wire of length l containing a current i by an external magnetic field B with angle θ w.r.t. l F = i · l · B · sin θ Galvanometro corrente elettrica da misurare molla di richiamo Mass spectrometer A particle of charge q and mass m in motion on an uniform magnetic field B perpendicular to the velocity v, undertakes a circular trajectory of ridius r = m·v q·B and angular q velocity ω = m B. Magnetic flow θ The flow of an homogeneous magnetic field B through a surface S whose normal direction forms an angle θ w.r.t. the direction of the magnetic field is: ΦB = B · S · cos θ Electromotive force (electric potential) induced � in a circuit by the variation of magnetic flux ∆ΦB concatenated to the circuit in a time interval ∆t ∆ΦB �=− ∆t the minus sign denotes the fact that the induced current is in opposition to the variation of the magnetic field ∆ΦB . Electric generator behavior opposite to the electric motor θ