Ampere force
Ampere force refers to the force experienced by two parallel current-carrying conductors due to their magnetic interaction. It is proportional to the product of the currents in the conductors and inversely proportional to the distance between them. This force is a fundamental concept in electromagnetism and is used to explain the behavior of current-carrying wires in magnetic fields.
8 Key excerpts on "Ampere force"
eBook - ePub- Adrian Waygood(Author)
- 2018(Publication Date)
- Routledge(Publisher)
...It follows, therefore, that if currents move through each of two, parallel conductors, then the resulting magnetic fields will react with each other, and produce a force between the two conductors. This force may be one of attraction or of repulsion, depending upon the relative directions of the electric currents in the conductors. If we apply Faraday’s properties of lines of magnetic flux, which we learnt from the chapter on magnetism (specifically, ‘parallel flux lines acting in the same direction repel other’, while ‘parallel flux lines acting in opposite directions cancel’) then, as illustrated in Figure 17.14, if the currents are drifting in opposite directions, the resulting force between them will be one of repulsion ; whereas if the currents are drifting in the same direction as each other, then the resulting force will be one of attraction. You will recall that the SI unit of electric current, the ampere, has been defined in terms of the force between two straight, parallel, current-carrying conductors. The above description explains the reason for this force. And these forces can be considerable. The exceptionally high fault currents that result from short-circuits in high-voltage power systems can actually cause severe distortion to any parallel conductors, such as busbars, carrying such currents. The forces between magnetic fields are very important in electrical engineering because, as we shall see, the operation of electric motors is entirely dependent upon these forces. Now let’s turn our attention to the behaviour of a current-carrying conductor, placed within a permanent magnetic field – such as that illustrated in Figure 17.15...
eBook - ePubFields of Force
The Development of a World View from Faraday to Einstein.
- William Berkson(Author)
- 2014(Publication Date)
- Routledge(Publisher)
...As mentioned above, the force between two current elements in Ampère’s theory is proportional to the strengths of the two currents and to the inverse square of the distance between the current elements—in analogy to Newton’s law of gravitation. The analogy to Newton breaks down because the force (a central force) is also a function of the angles between the two elements. In order to calculate the force between two currents (A and B) on Ampère’s theory, we must first add or integrate the effect of each current element of A on a particular element of B. If we thus work out the effect of A on each elment of B, and add the effects, we get the force of one current upon another. Ampère insisted on not applying his theory to open currents, as he was unable to carry out any experiments with them. Neumann thought that the induced currents must be some function of the already known ‘Ampèrian’ forces, and set out to find that function. 2 He was inspired in his idea by the theory of E. Lenz. Lenz had noticed that the forces due to induced currents were always such as to oppose the change in the forces existing before induction. 3 For example, if we have two like currents (which attract) and move them closer to each other, then the current induced will tend to decrease the attraction between the wires. By Ampère’s theory, the act of moving them closer together tends to increase the attraction. What Neumann discovered was that this mathematical function, giving the ‘electromotive’ forces causing the induced current, was the rate of change of the ‘potential’ of the force of one current upon the other. The ‘potential’ function was already a well-known function and the forces themselves were already calculable from Ampère’s theory...
eBook - ePub- C R Robertson(Author)
- 2008(Publication Date)
- Routledge(Publisher)
...The magnetic field produced at some distance d from its centre is shown in Fig. 5.18. Fig. 5.18 but in this case, N = 1 (one conductor) and ℓ = 2 πd metre (the circumference of the dotted circle), so Now, flux density B = μ 0 μ r H tesla, and as the field exists in air, then μ r = 1. Thus, the flux density at distance d from the centre is given by Consider now two conductors Y and Z carrying currents I 1 and I 2 respectively, at a distance of d metres between their centres as in Fig. 5.19. Fig. 5.19 Using equation [1] we can say that the flux density acting on Z due to current I 1 flowing in Y is: and the force exerted on Z = B 1 I 2 ℓ newton, or B 1 I 2 newton per metre length of Z. Hence, force/metre length acting on Z Now, the current I 2 flowing in Z also produces a magnetic field which will exert a force on Y. Using the same reasoning as above, it can be shown that: force/metre length acting on Y force exerted on each conductor = 2 × 10 −7 newton This value of force forms the basis for the definition of the ampere, namely: that current, which when maintained in each of two infinitely long parallel conductors situated in vacuo, and separated one metre between centres, produces a force of 2 × 10 −7 newton per metre length on each conductor. Worked Example 5.11 Q Two long parallel conductors are spaced 35 mm between centres. Calculate the force exerted between them when the currents carried are 50 A and 40 A respectively. A Worked Example 5.12 Q Calculate the flux density at a distance of 2 m from the centre of a conductor carrying a current of 1000 A. If the centre of a second conductor, carrying 300 A, was placed at this same distance, what would be the force exerted? A 5.8 The Moving Coil Meter Most analogue (pointer-on-scale) instruments rely on three factors for their operation: a deflecting torque; a restoring torque; and a damping torque. Deflecting Torque Essentially, a moving coil meter is a current measuring device...
eBook - ePub- S. Bobby Rauf(Author)
- 2020(Publication Date)
- CRC Press(Publisher)
...The positively or negatively charged particles at the atomic or molecular level are referred to as ions. The relationship between V, I, and R in the electrical circuit is governed by Ohm’s law. Ohm’s law, in conjunction with other basic electrical laws – used to analyze electrical circuits – will be explained in more detail in Chapter 2. For now, note that Ohm’s law is stated, mathematically, in the form of Eq. 1.41. In other words, according to Ohm’s law, electromotive force is equal to the product of current and resistance. E l e c t r o m o t i v e F o r c e, V = I ⋅ R = (C u r r e n t) × (R e s i s t a n c e) (1.41) The circuit shown in Figure 1.26b represents a basic electromagnetic circuit. This circuit consists of a toroid or donut-shaped core – typically constructed out of iron. In this magnetic circuit, a conductor, or wire, is wrapped in four turns around the left side of the toroid core. When current is passed through wound conductor, magnetic field is established in the core as represented by the dashed circular line, with an arrow pointing in clockwise direction. This magnetic field is referred to as magnetic flux, ф. Magnetic flux is measured in weber. The unit weber is named for the German physicist Wilhelm Eduard Weber (1804–1891). In the magnetic realm, the flux serves as a counterpart to the current, I, from the electrical realm. Just like the electromotive force, EMF, or voltage, drives the current through the resistor, R, the magnetomotive force (MMF), F, drives the magnetic flux, ф, through the toroid magnetic core. Magnetomotive force is measured in ampere-turns. In electrical systems, load is represented by the resistor R. In the magnetic circuit, the flow of magnetic flux is opposed by reluctance R. Just as Ohm’s law, represented by Eq. 1.41, governs the relationship between electromotive force (voltage), current, and resistance in the electrical realm, Eq...
eBook - ePub- Christopher Kitcher(Author)
- 2022(Publication Date)
- Routledge(Publisher)
...a Magnetic Field When a current carrying conductor is placed at right angles to a magnetic field, the force can be calculated by: F = BLI (Note it is taken for granted each letter has a multiplication sign between it and next letter.) where F is the force in newtons (N) B is the flux density (T) L is the effective conductor length (m) I is the current (A). EXAMPLE 1 A conductor 300mm long is placed in and at right angles to a magnetic field with a flux density of 0.5 tesla. Calculate the force exerted on the conductor when a current of 36A is passed through it. F = B × L × I F = 0.5 × 0.3 × 0.36 (note conversion from mm to m) = 5.4N EXAMPLE 2 A conductor 200mm long is placed in and at right angles to a magnetic field with a flux density of 0.35 tesla. Calculate the current required in the conductor to create a force of 5N on the conductor. F = B × L × I 5 = 0.35 × 0.2 × I Transpose for I I = 5 (0.35 × 0.2) = 71.42 A (n o t e u s e o f b r a c k e t s) Enter in calculator 5 ÷ (0.35 × 0.2) =...
eBook - ePubEnergy Medicine - E-Book
The Scientific Basis
- James L. Oschman(Author)
- 2015(Publication Date)
- Churchill Livingstone(Publisher)
...So far, electrons have resisted all attempts to find any hint of internal structure. We also know that the proton is 1836 times more massive than the electron. How can these two particles, the electron and the proton, with such a huge difference in mass, have identical charges? Again, we simply do not know what charge is, so we cannot answer this basic question. It is an important question because the charges of electrons and protons in an atom exactly cancel each other so that atoms can be electrically balanced or neutral. Magnetism from Electricity: Ampère’s Law If you are frustrated by the lack of precision of our knowledge at the basic level of electrons and protons, it will be comforting to know that the behaviour of these objects at larger scales is very reliable and predictable. They are so predictable that their behaviour is described by very well established physical laws. Laws are defined as scientific generalizations that are observations based on the behaviour of natural processes that are repeated again and again for many years. By definition, physical laws are statements about phenomena that are consistent: There have never been repeatable contradicting observations to refute them. Hence laws are solid enough that they are accepted universally within the scientific community. There are two physical laws that are of immense importance to energy medicine. The first is Ampère’s law, developed in 1826 by André-Marie Ampère (1775–1836). As a physical law, it is very reliable – no exceptions have been found in well over 150 years of physics research. Ampère’s law was devised to quantify an accidental discovery made in 1820 by Hans Christian Ørsted (1777–1851). While giving a physics demonstration at the University of Copenhagen, Ørsted noticed that electric currents flowing from a battery and through a wire caused nearby compass needles to wiggle when the battery was switched on and off (Figure 2.4)...
eBook - ePubElectromagnetics Explained
A Handbook for Wireless/ RF, EMC, and High-Speed Electronics
- Ron Schmitt(Author)
- 2002(Publication Date)
- Newnes(Publisher)
...This electric field manifests itself in the circuit as voltage. The opposing voltage persists until the current reaches its final steady-state value. The current, therefore, cannot change instantaneously, but continuously changes from zero to its final value over a period of time. Furthermore, while the current is increasing, a voltage drop exists across the wires. A voltage together with a current implies power loss. Although all real wires have resistive (heating) losses, you can ignore such losses for this example. The power loss encountered here actually corresponds to the power transferred into the magnetic field surrounding wires. Just as it takes energy to increase the speed of a car, it also takes energy to increase the speed of change in a circuit (i.e., the current). You can think of Lenz’s law as a way in which nature “balances its books.” Energy is always conserved, and Lenz’s law tells us how energy conservation is maintained with magnetic fields. FARADAY’S LAW Lenz’s law provides a qualitative understanding of how a changing magnetic field creates an electric field. Faraday’s law, proposed by 19th-century scientist Michael Faraday, describes this action qualitatively. For a solenoid with N turns and a cross sectional area A, Faraday’s law can be written as where dB/dt is the change in magnetic field per unit time and ν is the resulting voltage in the circuit. INDUCTORS At last it is time to learn about inductors. In contrast to the capacitor, which requires only one field (namely the electric field) to describe its operation, the inductor requires both fields to describe its operation even though it stores only magnetic energy. Here again is an inherent difference between the electric and magnetic fields. An inductor is a circuit element used to store magnetic energy. Typically, an inductor is created from several loops of wire stacked together to form a solenoid...
eBook - ePub- Donald W. McRobbie(Author)
- 2020(Publication Date)
- Wiley-Blackwell(Publisher)
...Charge moving within an external magnetic field produces an electric field by the hydrodynamic or Hall effect. Lorentz force The magnitude of the Lorentz force on a charge Q possessing velocity v is given as (2.20) The direction of the force can be determined by Fleming’s left‐hand rule. Magneto‐hydrodynamic effect A similar effect is the generation of an electric field E by the flow of charge within an external magnetic field (Figure 2.26). This is analogous to the Hall effect observed in semiconductors. (2.21) Figure 2.26 Magneto‐hydrodynamic and Hall effect. In terms of induced voltage or electrical potential, V, where (2.22) and d is the distance between charged surfaces (as in a capacitor), we have an induced voltage (2.23) The effect is most commonly encountered in MRI as an artefact in ECG traces. LAWS OF INDUCTION The laws of induction follow from Maxwell’s third equation or Faraday’s law. If we consider a wire loop within a time‐varying B‐field the magnitude of the induced E‐field is [ 3 ] (2.24) This applies for both the electric field induced by the imaging gradients responsible for peripheral nerve stimulation (PNS), and the electric field induced by the RF B 1 ‐field responsible for SAR and tissue (and implant) heating. The direction of E follows a left‐hand rule, as any magnetic field produced by the induced current in the wire opposes the rate of change of flux that induced it. Faraday induction from the gradients Biological tissues conduct electricity by means of water and electrolytes. Rather than considering electrical current in tissue (as in wires), we consider the current density J, a vector (Figure 2.27) (2.25) Figure 2.27 Ohm’s law in a circuit and a volume conductor. σ is the tissue conductivity in siemens per meter (S m −1). Some representative values are shown in Table 2.3. Table 2.3 Tissue conductivity at various frequencies...
