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Capacitors and Dielectrics

Inside the Keyboard-Insight: Inside the keyboard. Under each key of a keyboard we have a movable metal plate and a fixed plate, with a dielectric in between them. The dots are the places where the connection between the two conducting layers are made when the key is pressed. The lines shown in the image are electrical connections that allow tiny electric currents to flow when these layers are pressed. Lets learn more of such application oriented concepts about capacitors and dielectrics as we study this topic.

Learning objectives

After completing the topic, the student will be able to:

  • Understand and differentiate conductors and insulators.
  • Explore how charge is stored in an object.
  • Discuss, examine and explore as to why some elements, alloys or compounds conduct electricity more easily than other.
  • Explore the concept of capacitance of a capacitor and reflect on the types of capacitors.
  • Develop a theory to determine the energy stored in a capacitor and its applications in developing a computer chip.
  • Explore the working principle of the Van der Graaff generator, and its applications in producing large amount of static charge.
  • Understand the concept of dielectrics and its importance in using them to increase or decrease the capacitance.
Faraday cage Faraday's cage The cage is designed so that no discharges will reach inside.The minimal distance between the bars ensures that a discharge will always find it easier to hit a bar than pass in between to another object. The person inside is therefore protected. The discharge is created by a vast Van der Graaff generator (columns and spheres) behind the cage, with a potential difference of 2.5 million volts. Faraday cages are used to protect electrical equipment from lightning strikes.
Electrostatic equilibrium in conductors

A charged conductor tends to redistribute its excess charges evenly all around itself. We say that the conductor is in electrostatic equilibrium since there is no movement of charges. A conductor in electrostatic equilibrium shows the following properties:

  • There are no excess charges inside a conductor.
  • The charges reside only on the surface of the conductor.
  • The electric field on the surface of the conductor is perpendicular to the surface.
  • The electric fields are strongest at locations along the surface where the object is most curved.

Once a conductor is in electrostatic equilibrium, the electric field anywhere beneath the surface of a charged conductor is zero. If an electric field did exist beneath the surface of a conductor then the electric field would exert a force on the electrons present there. This net force would begin to accelerate and move these electrons. But since the conductor is in an electrostatic equilibrium, we should have no further motion of charge. So if this were to occur, then the original claim that the object was at electrostatic equilibrium would be a false claim. If the electrons within a conductor have assumed an equilibrium state, the net force upon those electrons is zero.

The electric field lines either begin or end upon a charge and in the case of a conductor, the charge exists solely upon its outer surface. The lines extend from this surface outward, not inward. This concept of the electric field being zero inside of a conducting surface was first demonstrated by Michael Faraday, a 19th century pioneer.

Faraday constructed a room within a room, covering the inner room with a metal foil. He sat inside the inner room (now known as the Faraday cage) with an electroscope and charged the surfaces of the outer and inner room using an electrostatic generator. While sparks were seen flying outwards from the walls of the outer room, there was no detection of an electric field within the inner room. This clearly showed that charges in a conductor reside solely on its outer surface. Inside a closed conductor, the electric field is zero.

Any closed, conducting surface can serve as a Faraday’s cage, shielding anything that surrounds from the potentially damaging effects of electric fields. This principle of electrical shielding is commonly utilized today. We protect delicate electrical equipment by enclosing them in metal foils or cases. Even delicate computer chips and other components are shipped inside of conducting plastic packaging, which shields the chips from electric fields. In spacecrafts and satellites many delicate electrical components are separated from each other by electrical shielding so that functioning of one does not affect the other component.

conducting curved surface Demonstration of electric field for a conducting curved surface. Electric field will always be perpendicular to the curved surface of a conductor.
Electric field in a conductor

Electric field is always perpendicular to the conductor's surface, which is in electrostatic equilibrium. If there were a component of electric field directed parallel to the surface, then the excess charge on the surface would have a force that would accelerate the charges. If a charge is set into motion, the object is not in a state of electrostatic equilibrium.

Therefore, the electric field must be perpendicular to the conducting surface for objects, which are in electrostatic equilibrium. Certainly a conducting object which has recently acquired an excess charge has a component of electric field and electric force parallel to the surface; it is this component which acts upon the excess charge to distribute the excess charge over the surface until electrostatic equilibrium is reached. Once reached, there is no longer any parallel component of electric field and any motion of excess charge.

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