Принцип суперпозиции сил

Электрическая сила, как и все силы, является векторной величиной. Поэтому, когда на заряд действуют силы двух или более источников, суммарная действующая на него сила – это просто векторная сумма сил взятых по отдельности. Например, на рисунке 19-8,суммарная сила F1, действующая на заряд q1 является векторная сумма сил от зарядов 2, 3, 4:

F1 = F12 + F13 + F14

Это называется суперпозицией сил.

Обратите внимание, что суммарная сила, действующая на данный заряд, равна сумме взаимодействия в то время, в которое сила между каждой парой зарядов определяется законом Кулона. Например, полная сила, действующая на заряд r на рисунке 19-R равна сумме сил, действующих между Q1 и Q2, Q1 и Q3 и Q1 и Q4. Таким образом, наложение сил можно рассматривать как обобщение закона Кулона для систем, содержащих более двух зарядов. В нашем первом численном примере принципа суперпозиции, мы рассмотрели три заряда на одной линии.

J. Zumerchik-Macmillan. Encyclopedia of Energy. Vol.1.
“Electric motor systems”

Electric motors are everywhere. These ubiquitous devices come in a wide variety of sizes and power outputs, ranging from a fraction of a watt to huge multikilowatt applications. Tiny ones operate com­puter disk drives, power windows/mirrors, and wind­shield wipers; moderate-sized ones run appliances such as fans, blenders, electric shavers, and vacuum cleaners; a large drive pumps, elevators, sawmills, and electric trains and vehicles.

There has been not only growth in the total num­ber of electric motors (more standard appliances in use), but also a proliferation in their use for new, novel applications. Both trends will continue to increase demand for the electricity to run electric motors. In the United States, electric motors are responsible for consuming more than half of all electricity, and for the industrial sector alone, close to two-thirds. Since the cost of the electricity to power these motors is enor­mous (estimated at more than $90 billion a year), research is focused on finding ways to increase the energy efficiency of motors and motor systems.

EARLY DEVELOPMENT

Electric motors are devices that convert electrical energy into mechanical energy. Devices that do the opposite—convert mechanical energy into electrical energy—are called generators. An important example is power plants, where large gas, steam, and hydro­electric turbines drive generators to provide electric­ity. Since generators and motors work under the same principles, and because construction differences are minimal, often generators can function as motors and motors, as generators, with only minor changes. The early development of electric motors and gen­erators can be traced to the 1820 discovery by Hans Christian Oersted that electricity in motion generates a magnetic field. Oersted proved the long-suspected promise that there is indeed a relationship between electricity and magnetism. Shortly thereafter, Michael Faraday built a primitive electric motor, which showed that Oersted's effect could be used to produce continuous motion.

Electric motors consist of two main parts: the rotor, which is free to rotate, and the stator, which is stationary (Figure 1). Usually each produces a mag­netic field, either through the use of permanent mag­nets, or by electric current flowing through the electromagnetic windings (electromagnets produce magnetism by an electric current rather than by per­manent magnets). It is the attraction and repulsion between poles on the rotor and the stator that cause the electromagnet to rotate. Repulsion is at a maxi­mum when the current is perpendicular to the mag­netic field. The left side of the rotator receives an upward push and the right side receives a downward push; thus rotation occurs in a clockwise direction. When the plane of the rotator is parallel to the magnetic field (as in Figure 1) there is no force on the sides of the rotator. When the rotator is perpendicular to the magnetic field, forces are exerted on all its sides equally, canceling out. Therefore, to produce contin­uous motion, the current must be reversed when reaching a vertical direction. For alternating-current motors this occurs automatically, since the alternat­ing magnetic attraction and repulsion change direc­tions 120 times each second; for direct current-motors, this usually is accomplished with a device called a commutator.

Before useful electric motors could be developed, it was first necessary to develop practical electromag­nets, which was primarily the result of work done by Englishman William Sturgeon as well as Joseph Henry and Thomas Davenport of the United States. In 1873 Zenobe-Theophile Gramme, a Belgian-born electrical engineer, demonstrated the first commercial electric motor. A decade later Nikola Tesla, a Serbian-American engineer, invented the first alternating-cur­rent induction motor, the prototype for the majority of modern electric motors that followed. Magnetic fields today are measured in units of teslas (symbol T), to acknowledge Tesla's contribution to the field.

MOTOR TYPES

The electrical power supplied to electrical motors can be from a direct-current (dc) source or an alternat­ing-current (ac) source. Because dc motors are more expensive to produce and less reliable, and because standard household current is ac, ac motors are far more prevalent. However, the growing demand for portable appliances such as laptop computers, cord­less power drills, and vacuums ensures a future for dc motors. For these portable applications, the alternat­ing current charges the battery, and the direct current of the battery powers the dc motor.

Based on the way magnetic fields are generated and controlled in the rotor and the stator, there are several additional subclassifications of direct- and alternating-current motors.

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