The Battery Revisited

Earlier in this chapter, during the introduction of voltage, I mentioned that a neutral conductor like a wire or metal plate that is brought close to a battery will not be affected by the battery. Even if the battery or Figure 2.15 Electric field of DC voltage across a conducting wire. Arrowheads show the direction of the electric field. Voltage is shown by shade inside the conductor and as contours outside the conductor. This figure was created using Ansoft Corporation's Maxwell 2D field...

Even a Stationary Charge Has a Magnetic Field

A stationary charge has a magnetic field. This statement may seem to be a contradiction to what you have already learned about magnetic fields. Only moving charges produce magnetic fields, right Let me explain. Imagine yourself sitting in a wagon rolling along at a steady, constant speed. You have a charge in front of you. You measure it and it has an electric field but no magnetic field. You say I am wrong. But then you jump off the wagon, and you are on the ground. The charge is now moving...

Electric Field And Magnetic Field Become The Electromagnetic Field

The 4-vector concept also allows us to condense the mathematics of electromagnetics, and reveals the true nature of the electromagnetic field. By combining the magnetic vector potential with voltage into a four vector A Ax,Ay,Az,V c , a single electromagnetic potential is formed. Using this 4-potential, the electric and magnetic fields combine to form a single electromagnetic field, which can be represented by a mathematical object called a tensor. In the mathematical system called Clifford...

The Field Of An Alternating Current

If we allow the voltage source across a wire to slowly oscillate in time at frequency, fo, the accompanying electric field will take the same form as that of the DC charge, except that the magnitude will vary between positive and negative values (see Figure 5.8). Relating frequency to wavelength by l c f, we define slow oscillation as any frequency whose corresponding wavelength is much greater than the length of the wire. This condition is often called quasi-static. In this case, the current...

The Moving Charge

Right Hand Rule Electromagnetics

Another, more fundamental, test particle for the magnetic field is a free charge moving with velocity, v. As you learned earlier in this chapter, the magnetic field arises from moving charges. Therefore, a moving charge serves as a good test particle. You can better understand the effect that a magnetic field has on a moving charge by first understanding a similar mechanical effect, that of the Coriolis force. Without knowing it, you are probably very familiar with the Coriolis force. Imagine...

The Electromagnetic Spectrum

For electrical engineers the word electromagnetics typically conjures up thoughts of antennas, transmission lines, and radio waves, or maybe boring lectures and all-nighters studying for exams. However, this electrical word also describes a broad range of phenomena in addition to electronics, ranging from X-rays to optics to thermal radiation. In physics courses, we are taught that all these phenomena concern electromagnetic waves. Even many nontechnical people are familiar with this concept...

Circuits As Guides For Waves And Sparameters

In the previous chapter, I mentioned that waves do not propagate well in conductors. They attenuate down to miniscule levels after traveling a few skin depths. Keep in mind that the conductor actually becomes more lossy at higher frequencies because the current must travel through a smaller cross-sectional area. High-voltage power lines often use multiple parallel wires for each phase partly because of the skin effect. At 60 Hz, the skin depth is about 8 mm. By splitting the current into...

Explanation Of The Magnetic Vector Potential

In Chapter 3, I promised to give a conceptual meaning to the magnetic vector potential. This explanation involves the electrons of a superconducting circuit. In a superconductor, the electrons can move freely without colliding with the positive ions of the metal. Suppose that a DC current is applied to a superconducting wire. Without collisions, the electrons form a collective system that has a wave nature. In other words, the wave nature of the electrons dominates over the particle nature....

Power Supply Decoupling Problems And Techniques

Decoupled Supply

Power supply decoupling is the term given to the technique of making sure the DC power line variations do not affect the loads amplifier, ICs, logic gates, etc. and vice versa. Since most ICs have AC signals as inputs and outputs, the current drawn from the power supply will vary in an AC manner. For example, an RF circuit that amplifies a 900 MHz signal will draw a supply current that varies at 900 MHz. A digital CMOS circuit that buffers a 100 MHz digital signal will also draw a supply...

The Quantum Vacuum And Virtual Photons

Now what about the energy in nonradiating electromagnetic fields, that is, the static field and the near field Quantum physics states that any energy must consist of individual packets or quanta, but this implies that even the static field must consist of particles. In fact, the static field does consist of particles virtual photons. To explain virtual photons, let's step further into the strange world of quantum physics. If we think about the uncertainty principle from another point of view,...

The Field Of A Static Charge

Electromagnetic Static Field Cells

For a single charged particle, such as an electron, the electric field forms a simple radial pattern as shown in Figure 5.4. By convention, the field Figure 5.4 The static field of a positive charge is shown as a vector plot top left , streamline plot middle left , and a contour plot bottom left . The static field of a dipole is shown as a vector plot top right , streamline plot middle right , and contour plot bottom right . Figure 5.4 The static field of a positive charge is shown as a vector...

And Maxwell Said Let There Be Light

In addition to being a physicist, Maxwell was also an extraordinarily talented mathematician. When he added his new term to the existing equations for electricity and magnetism, he quickly noticed that the mathematics implied that propagating electromagnetic waves could be created. Such waves had never been observed. This was a monumental discovery. Furthermore, when he performed the mathematical derivations, the speed of these new waves was predicted to be that of the speed of light Before...

Near And Far Field

As mentioned earlier, an AC circuit will have a reactive field and a radiating field. The reactive field of an AC source circuit or system is often referred to as the near field because it is concentrated near the source. Similarly, the radiating field is referred to as the far field because its effects extend far from the source. Let's examine why. The power density of an electromagnetic field at a distance, r, from the source can be represented by a series in 1 r, Field power density Pd Q r2...

Electrostatic Induction And Capacitance

To understand capacitance, you need to first understand the process of electrostatic induction. For example, consider that you have a metal ball that is positively charged, near which you bring a neutral metal ball. Even though the second ball has overall neutrality, it still contains many charges. Neutrality arises because the positive and negative charges exist in equal quantities. When placed next to the first ball, the second ball is affected by the electric field of the charged ball. The...

Mesh Shields and Faraday Cages

Due to the radiation limiting effects of small apertures, shields can be made from a mesh of wires or from a metallic cage, as an alternative to using a solid sheet of metal. From the results of apertures, you can deduce that the holes in the mesh or cage should be considerably less than half a wavelength for such shields to work properly. Moreover, the mesh will be mostly transparent to signals with wavelengths smaller than the mesh holes. When the shield takes the form of a wire cage, it is...

Antenna Pattern Versus Electrical Length

Dipole Radiation

Antennas do not radiate equally to all directions. The directional dependence of antenna radiation is aptly called the antenna pattern. An electric dipole that is 1 2 1 in length or smaller exhibits a fairly simple antenna pattern. The most power is radiated in the direction broadside to the antenna that is, perpendicular to the antenna's length. The power decreases with decreasing angle such that at zero degrees, no power is radiated. In other words, no power is radiated in the direction of...

Conducted Versus Induced Versus Radiated Interference

High Frequency Interference

In EMC literature and EMC regulations the mechanisms of electromagnetic interference are divided into two categories, conducted and radiated. Historically, this categorization has been used in the regulations and, unfortunately, it continues today. I use the word unfortunately because both near-field coupling and far-field radiation are lumped under the term radiated emissions. While experts in electromagnetics are quite familiar with the difference between near-field coupling and far-field...

Differential Mode And Common Mode Radiation

Decoupling Capacitor Ground

Unintentional radiation can be described as either differential mode or common mode. The two terms relate to the currents that create the radiation. Differential mode currents are equal but travel in opposite directions. Common mode currents travel in the same direction. On any transmission line, the signal current and the return current travel in opposite directions. As long as the two currents are close together the radiation is very small, albeit non-zero. The two currents Figure 12.18 Here...

Voltage And Potential Energy

A quantity that goes hand in hand with the electric field is voltage. Voltage is also called potential, which is an accurate description since voltage quantifies potential energy. Voltage, like the electric field, is normalized per unit charge. Voltage Potential energy of a unit charge In other words, multiplying voltage by charge gives the potential energy of that charge, just as multiplying the electric field by charge gives the force felt by the charge. Mathematically we represent this by...

The Path Of Least Impedance

Via Inductance High Speed Design Rules

One of the most fundamental relations taught in basic circuit theory is that current follows the path of least resistance. At high frequencies this relation is modified to current follows the path of least impedance. The path of least resistance and the path of least impedance may or may not be the same, depending on the circuit geometry and the signal frequency. In any circuit, the signal consists of the flow of two currents, typically called the signal and return. Since the return current...

Static Electricity And Lightning

Static Electricity Free Energy

Let's go back to the charged sphere of Figure 2.5. If the second metal ball is placed closer to the charged ball so that they actually touch, the Figure 2.11 A Water molecule. B Water molecules in random orientation with no field applied. C Water molecules line up when an electric field is applied. Figure 2.11 A Water molecule. B Water molecules in random orientation with no field applied. C Water molecules line up when an electric field is applied. negative charge will now redistribute itself...

The Vector Magnetic Potential And Potential Momentum

Magnetic Vector Potential

In the previous chapter, which covered electric fields, one of the first concepts covered was the electric field potential, more commonly known as voltage. You may be wondering if a similar potential exists for the magnetic field. If so, you are correct. However, the magnetic potential is a vector quantity. It has both magnitude and direction. The vector potential around a current is shown in Figure 3.16. As you can see, its main characteristic is that it points in a direction parallel to the...