Ampere's Law Magnetic Field
Ampere's Law describes the relationship between the magnetic field around a closed loop and the current passing through the loop. It states that the magnetic field is proportional to the current enclosed by the loop. This law is a fundamental principle in electromagnetism and is used to calculate the magnetic field produced by current-carrying conductors.
8 Key excerpts on "Ampere's Law Magnetic Field"
eBook - ePubEnergy Medicine - E-Book
The Scientific Basis
- James L. Oschman(Author)
- 2015(Publication Date)
- Churchill Livingstone(Publisher)
...One reason Ampère’s law is so important for energy medicine is that it explains the origin of the biomagnetic field surrounding the human body. As will be described in Chapter 5. See Figure 5.17, the various organs in the body generate electrical currents that flow through the tissues and therefore generate magnetic fields both within and around the body. Figure 2.5 André-Marie Ampère (1775–1836). The strongest electrical field is produced by the heart and generates a current that flows through the circulatory system, which is a good conductor. In accord with Ampère’s law, this current produces the strongest biomagnetic field of the body (Figure 2.6). This point is important because of the skepticism about energy fields around the body that are described and used by various complementary and alternative medicine (CAM) practitioners. The laws of physics require the production of a biomagnetic field around the body as a result of the electrical activity of the heart and other organs. In Chapter 8 we will see the methods that have been used to measure these biomagnetic fields. Figure 2.6 The strongest electrical field is produced by the heart and generates an electrical field that is conducted throughout the body via the circulatory system (A), which is a good conductor. The electrical field of the heart is recorded in the electrocardiogram (B). In accord with Ampère’s law, this current produces the strongest biomagnetic field of any organ, and the field is radiated into the space surrounding the body (C). Modern devices can record the biomagnetic field of the heart, which is called a magnetocardiogram (D). Biomagnetic fields are discussed in detail in Chapter 8. Electricity from Magnetism: Faraday’s Law of Induction About 11 years after Ørsted’s important discovery in Denmark, another important finding took place simultaneously in England and America...
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- 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...
- G. Jagadeeswar Reddy, T. Jayachandra Prasad(Authors)
- 2020(Publication Date)
- CRC Press(Publisher)
...differential length, and the sine of the angle lying between the element and a line connecting the element to the point P where the field is desired, (b) Inversely proportional to the square of the distance from the differential element to the point P. (c) Directly proportional to the constant of the medium (µ) and (d) Directed normal to the plane containing the differential element and the line drawn from the filament to the point P. B = ∫ μ I d l sin θ 4 π r 2 Wb/m 2 6. State Ampere’s law for a magnetic field. The Ampere’s law states that the line integral of H around a single closed path is equal to the current enclosed. It can also be stated as the line integral of B around a single closed path is equal to the permeability of the medium times the current enclosed. ∫ H ⋅ d l = I ∫ B ⋅ d l = μ I 7. What is the force between two current carrying conductors? The force between the two conductors carrying current I 1 and I 2 separated by. a distance r is given by F = μ 0 I 1 I 2 2 π r N 8. Give the relation between magnetic flux density and magnetic field intensity. The permeability of any medium is the ratio of the magnetic flux density B to the magnetic field intensity H. μ = B H H/m 9. State the Gauss’s law for magnetic fields. The integral of the magnetic flux density B over a closed surface is zero. This is called the Gauss’s law for magnetic fields. ∮ B ⋅ d S = 0 where, dS is the normal component of the surface. 10. What is the torque on a current carrying loop? The torque, or moment, of a force is a vector whose magnitude is the product of the magnitudes of the vector force, the vector lever arm, and the sine of the angle between these two vectors...
eBook - ePub- C R Robertson(Author)
- 2008(Publication Date)
- Routledge(Publisher)
...However, if it was refined and performed under controlled conditions, then it would yield the following results: The magnitude of the induced emf is directly proportional to the value of magnetic flux, the rate at which this flux links with the coil, and the number of turns on the coil. Expressed as an equation we have: Notes: 1 The symbol for the induced emf is shown as a lower-case letter e. This is because it is only present for the short interval of time during which there is relative movement taking place, and so has only a momentary value. 2 The term dΦ/d t is simply a mathematical means of stating ‘the rate of change of flux with time’. The combination N Φ/d t is often referred to as the ‘rate of change of flux linkages’. 3 The minus sign is a reminder that Lenz’s law applies. This law is described in the next section. 4 Equation (5.1) forms the basis for the definition of the unit of magnetic flux, the weber, thus: The weber is that magnetic flux which, linking a circuit of one turn, induces in it an emf of one volt when the flux is reduced to zero at a uniform rate in one second. In other words, 1 volt = 1 weber/second or 1 weber = 1 volt second. 5.2 Lenz’s Law This law states that the polarity of an induced emf is always such that it opposes the change which produced it. This is similar to the statement in mechanics, that for every force there is an opposite reaction. 5.3 Fleming’s Righthand Rule This is a convenient means of determining the polarity of an induced emf in a conductor. Also, provided that the conductor forms part of a complete circuit, it will indicate the direction of the resulting current flow. The first finger, the second finger and the thumb of the right hand are held out mutually at right angles to each other (like the three edges of a cube as shown in Fig. 5.3)...
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...
- Magno Urbano(Author)
- 2019(Publication Date)
- Wiley(Publisher)
...We will know why in the following paragraphs. Figure 9.1 Ørsted experiment (open circuit). Figure 9.2 Ørsted experiment (switch closed). Figure 9.3 Ørsted experiment (battery is inverted). Keeping the compasses below the wire and inverting the battery make current flow in the opposite direction, giving rise to a magnetic field with an opposite direction. This will force the compasses to rotate 180° to point to the new magnetic field direction, as shown in Figure 9.3. Once more, placing the compasses over the wire will make their needles point to the opposite direction. Magnetic fields have a specific orientation that depends on the current flow direction. To find the magnetic field orientation, we can use the right‐hand rule. 9.4 The Right‐Hand Rule Imagine a right hand grabbing a wire. The thumb points to the current flow direction as illustrated by the black arrow pointing up in Figure 9.4. Figure 9.4 Right‐hand rule. For a right hand grabbing a wire like this, the magnetic field circulates the wire and points in the direction of the other fingers, as illustrated in Figure 9.4. The right‐hand rule helps to find the magnetic field orientation in a wire. Magnetic fields are normally designated in technical literature by the uppercase letter B and have the circular form, shown in Figure 9.5, for a current flowing in the direction of I. Figure 9.5 Magnetic field created by a current flow. The rise of a magnetic field by a current flow shows a connection between electricity and magnetism. One cannot exist without the other...
