## 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 charges of the second ball separate. Negative charges are attracted, and positive charges are repelled, leaving the second ball polarized, as shown in Figure 2.5. This polarization of charge is called electrostatic induction.

A direct consequence of electrostatic induction is that the electric field inside an unconnected conductor is always zero at steady state. When a conductor is first placed in a field, the field permeates the conductor. The charges then separate as described in the preceding paragraph. The separation of charge tends to neutralize the electric field. Charge movement continues until the electric field reaches zero. Another way of stating this is that the voltage inside a conductor is constant at steady state. Placed in an ambient electric field, the conductor quickly adjusts its charge configuration until it has reached the voltage potential of its environment.

Now let's connect a metal object to the second ball using a wire. As shown in Figure 2.6, the charge polarizes even further, with the negative charge of the neutral objects moving as far away as possible. Figure 2.7 takes this one step further by connecting the earth to the second ball. (An earth connection can be achieved by connecting the ball to the third prong of a wall outlet, which typically is "earthed" on the

Figure 2.5 A) A negatively charged metal sphere. B) A neutral sphere (right) is brought close to the negative sphere (left).

Figure 2.5 A) A negatively charged metal sphere. B) A neutral sphere (right) is brought close to the negative sphere (left).

Figure 2.6 A second neutral object is connected by a wire.

outside of each building using 8 foot or longer copper stakes.) Here the negative charge will move down the wire, into the earth, and go very far away.

Instead of placing a constant charge on the first metal ball, you could connect an oscillating charge, as in Figure 2.8. For example, assume that the AC voltage is at a frequency of 60 Hz; the polarization induced

Figure 2.7 The neutral sphere is connected to ground with a wire.

 -I \ //////////////////////////////// + ++ ----_-_ ^^

Figure 2.8 An AC source is connected to the first sphere.

Figure 2.8 An AC source is connected to the first sphere.

in the second ball will alternate at a frequency of 60 Hz. The alternating polarization will also cause current to flow in the wire that connects the second ball to the ground. What you have created is simply a capacitor! Any metal conductors that are separated by an insulator form a capacitor. In Figure 2.9, the two balls have been replaced with metal plates, forming a more familiar and efficient capacitor. Notice that no current actually traverses the gap between the plates, but equal current flows on both sides, as charge rushes to and from the plates of the capacitor. The virtual current that passes between the plates is called displacement current. It is really just a changing electric field, but we call it a current.

You can get a good feel for electrostatic induction by learning how some simple, but ingenious, inventions work. If you have ever worked

ELECTROSTATIC INDUCTION AND CAPACITANCE Figure 2.9 Spheres are replaced by metal plates.

Figure 2.10 Block diagram for a non-contact field detector.

on the electric mains wiring that runs in the walls of your house and provides the 120V power to your electric outlets and lamps, you have probably purchased what is called a non-contact field detector. (Incidentally, the term "mains" refers to the fact that your power is provided by your electric utility company. The same term is also used for the water that enters your house from the water utility.) A non-contact field detector is a device that is about the size and shape of a magic marker. It allows you to determine if a wire is live (is connected to voltage) or not without actually making metallic contact. This nifty invention can be waved near insulated wires, or it can be inserted into an electric outlet. It detects live wires and live outlets using the phenomenon of electrostatic induction that you just learned about. A simple schematic of such a device is shown in Figure 2.10. A metal lead or plate is attached to the input of a high-impedance amplifier. This plate serves one side of a capacitor. When the plate is brought close to an object that has an electric field, charge is induced on the plate. Some of the charge has to pass through the amplifier. Because the amplifier has high input impedance, a reasonable voltage will be created at its output. If the object being tested has a varying electric field, like a wall outlet, an AC current will be induced in the device. The rest of the circuitry serves to light an LED when the induced current varies continuously at around 60 Hz.

A variation of this circuit uses a human as the capacitive plate of the device. Glow tube meters and zero-pressure "touch" buttons work in this manner. A glow tube meter is a device for testing electrical outlets. It looks like a screwdriver, except the handle is made of clear plastic and contains a small glow tube inside. The glow tube is a glass tube filled with neon gas and contains two separated electrodes. One electrode is connected to the screwdriver blade and makes contact inside the electric outlet. The other electrode is connected to a piece of metal at the end of the screwdriver handle. By touching your finger to the handle end, you become part of a circuit. Being a decent conductor, your body serves the function of being one half of a capacitor. A small amount of the 60 Hz displacement current (~10 ||A) is able to capacitively couple from your body to the ground wires in the wall. This small current causes a voltage drop across you and across the glow tube. The gas inside the glow tube ionizes and conducts electricity. In the process, it gives off a faint orange glow, telling you that the outlet is working. You certainly should use care with such a device, and be sure not to touch the screwdriver shaft directly.

Touch buttons are found in some elevators. These buttons are metal, and if you encounter one, you will notice that the button does not physically depress when you touch it. This button is connected to a high-impedance amplifier. When you touch the button, you again form a capacitor plate. In this application, your body couples 60 Hz energy from the wires in the elevator and the fluorescent lights on the ceiling to the metal touch pad. A high-impedance amplifier amplifies the current and determines that you have, for instance, touched the button for the third floor.

It may be tempting to think of these applications as antennas picking up 60 Hz radiation, but this idea is incorrect. Being electrically small wires, virtually no energy is radiated. In addition, you are standing well within the near field of the source. These topics are discussed in detail in Chapter 5.

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