dcpmm_basics

# dcpmm_basics - Magnetic electro-mechanical machines Neville...

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Magnetic electro-mechanical machines Neville Hogan This is a brief outline of the physics underlying simple electro-magnetic machines, especially the ubiquitous direct-current permanent-magnet motor. Lorentz Force A magnetic field exerts force on a moving charge. The Lorentz equation: f = q( E + v × B ) where f : force exerted on charge q E : electric field strength v : velocity of the moving charge B : magnetic flux density Consider a stationary straight conductor perpendicular to a vertically-oriented magnetic field. Magnetic flux B F i Current Force Stationary conductor Motion of charges Figure 1: Forces on a current-carrying conductor in a magnetic field. An electric field is oriented parallel to the wire. As charges move along the wire, the magnetic field makes them try to move sideways, exerting a force on the wire. The lateral force due to all the charge in the wire is: f = ρ Al ( v × B ) where ρ : density of charge in the wire (charge per unit volume) l: length of the wire in the magnetic field A: its cross-sectional area The moving charges constitute a current, i i = ρ A v The lateral force on the wire is proportional to the current flowing in it. f = l ( i × B ) © Neville Hogan page 1

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For the orthogonal orientations shown in the figure, the vectors may be represented by their magnitudes. f = l B i This is one of a pair of equations that describe how electromagnetic phenomena can transfer power between mechanical and electrical systems. The same physical phenomenon also relates velocity and voltage. Consider the same wire perpendicular to the same magnetic field, but moving as shown Magnetic flux B Moving conductor Electro-motive force Motion of charges Velocity v Figure 2: Voltage across a conductor moving in a magnetic field. A component of charge motion is the same as the wire motion. The magnetic field makes charges try to move along the length of the wire from left to right. The resulting electromotive force (emf) opposes the current and is known as back-emf. The size of the back-emf may be deduced as follows. Voltage between two points is the work
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## This note was uploaded on 02/27/2012 for the course MECHANICAL 2.141 taught by Professor Nevillehogan during the Fall '06 term at MIT.

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dcpmm_basics - Magnetic electro-mechanical machines Neville...

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