Electricity PDF

Chapter Three Electricity Prepared by Dr. Mohamed Hasabelnaby Lecturer of physics, School of Allied Health Sciences, Badr University. 3.1 Properties of Electric Charges A number of simple experiments demonstrate the existence o...

Chapter Three Electricity Prepared by Dr. Mohamed Hasabelnaby Lecturer of physics, School of Allied Health Sciences, Badr University. 3.1 Properties of Electric Charges A number of simple experiments demonstrate the existence of electric forces and charges. For example:  After running a comb through your hair on a dry day, you will find that the comb attracts bits of paper. The attractive force is often strong enough to suspend the paper.  The same effect occurs when certain materials are rubbed together, such as glass rubbed with silk or rubber with fur.  Rub an inflated balloon with wool, the balloon then adheres to a wall, often for hours. When materials behave in this way, they are said to be electrified, or to have become electrically charged. You can easily electrify your body by vigorously rubbing your shoes on a wool rug. Evidence of the electric charge on your body can be detected by lightly touching (and startling) a friend, under the right conditions, you will see a spark when you touch, and both of you will feel a slight tingle. It was found that there are two kinds of electric charges, which were given the names positive and negative by Benjamin Franklin (1706–1790). We identify negative charge as that type possessed by electrons and positive charge as that possessed by protons. To verify that there are two types of charge, suppose a hard rubber rod that has been rubbed with fur is suspended by a sewing thread, as shown in Figure (3.1). When a glass rod that has been rubbed with silk is brought near the rubber rod, the two attract each other (Fig. 3.1a). On the other hand, if two charged rubber rods (or two charged glass rods) are brought near each other, as shown in Figure (3.1b), the two repel each other. This observation shows that the rubber and glass have two different types of charge on them. On the basis of these observations, we conclude that charges of the same sign repel one another and charges with opposite signs attract one another. Fig. (3.1) (a) A negatively charged rubber rod suspended by a thread is attracted to a positively charged glass rod. (b) A negatively charged rubber rod is repelled by another negatively charged rubber rod.  Another important aspect of electricity that arises from experimental observations is that electric charge is always conserved in an isolated system. That is, when one object is rubbed against another, charge is not created in the process. The electrified state is due to a transfer of charge from one object to the other. One object gains some amount of negative charge while the other gains an equal amount of positive charge. For example, when a glass rod is rubbed with silk, the silk obtains a negative charge that is equal in magnitude to the positive charge on the glass rod. 3.2 Charging Objects by Induction It is convenient to classify materials in terms of the ability of electrons to move through the material: Electrical conductors are materials in which some of the electrons are free electrons that are not bound to atoms and can move relatively freely through the material; Electrical insulators are materials in which all electrons are bound to atoms and cannot move freely through the material. Semiconductors are a third class of materials, and their electrical properties are somewhere between those of insulators and those of conductors. Silicon and germanium are well-known examples of semiconductors. Materials such as glass, rubber, and wood fall into the category of electrical insulators. When such materials are charged by rubbing, only the area rubbed becomes charged, and the charged particles are unable to move to other regions of the material. In contrast, materials such as copper, aluminum, and silver are good electrical conductors. When such materials are charged in some small region, the charge readily distributes itself over the entire surface of the material. To understand how to charge a conductor by a process known as induction,  Consider a neutral (uncharged) conducting sphere insulated from the ground as shown in Figure (3.2a). There are an equal number of electrons and protons in the sphere, so the charge on the sphere is exactly zero.  When a negatively charged rubber rod is brought near the sphere, electrons in the region nearest the rod experience a repulsive force and migrate to the opposite side of the sphere. This migration leaves the side of the sphere near the rod with an effective positive charge because of the diminished number of electrons as in Figure (3.2b).  If a wire connected from the sphere to the Earth (Fig. 3.2c), some of the electrons in the conductor are so strongly repelled by the presence of the negative charge in the rod that they move out of the sphere through the wire and into the Earth.  If the wire to ground is then removed (Fig. 3.2d), the conducting sphere contains an excess of induced positive charge because it has fewer electrons than it needs to cancel out the positive charge of the protons.  When the rubber rod is removed from the vicinity of the sphere (Fig. 3.2e), this induced positive charge remains on the ungrounded sphere. Notice that the rubber rod loses none of its negative charge during this process. Fig. (3.2): Charging a metallic object by induction. Charging an object by induction requires no contact with the object inducing the charge. That is in contrast to charging an object by rubbing (that is, by conduction), which does require contact between the two objects. A process similar to induction in conductors takes place in insulators. In most neutral molecules, the center of positive charge coincides with the center of negative charge. In the presence of a charged object, however, these centers inside each molecule in an insulator may shift slightly, resulting in more positive charge on one side of the molecule than on the other. This realignment of charge within individual molecules produces a layer of charge on the surface of the insulator as shown in Figure (3.3a). The proximity of the positive charges on the surface of the object and the negative charges on the surface of the insulator results in an attractive force between the object and the insulator. Your knowledge of induction in insulators should help you explain why a charged rod attracts bits of electrically neutral paper as shown in Figure (3.3b). Fig. (3.3) (a) A charged balloon is brought near an insulating wall. (b) A charged rod is brought close to bits of paper. 3.3 Coulomb's law Coulomb's law is a law of physics describing the electrostatic interaction between electrically charged particles. It was studied and first published in 1783 by French physicist Charles Augustin de Coulomb and was essential to the development of the theory of electromagnetism. Coulomb's law states that: "The magnitude of the Electrostatics force of interaction between two point charges is directly proportional to the scalar multiplication of the magnitudes of charges and inversely proportional to the square of the distances between them." Consider a system of two point charges, q1 and q2, separated by a distance r in vacuum. The force exerted by on is given by Coulomb's law: ⃓𝒒𝟏 ⃓⃓𝒒𝟐 ⃓ F12 = ke (3.1) 𝒓𝟐 Where r is the separation distance and ke is proportionality constant. A positive force implies it is repulsive, while a negative force implies it is attractive. The proportionality constant ke, called the Coulomb constant (sometimes called the Coulomb force constant), The value of the Coulomb constant depends on the choice of units. The SI unit of charge is the coulomb (C). The Coulomb constant ke in SI units has the value Ke= 5 8.987 6 3 109 N.m2/C2 This constant is also written in the form: 1 𝑘𝑒 = 4𝜋𝜀0 Where the constant 𝜀0 (Greek letter epsilon) is known as the permittivity of free space and has the value: 𝜺𝟎 = 5 8.854 2 3 1012 C2/N. m2  Fig. (3.4): Two point charges separated by a distance r exert a force on each other that is given by Coulomb’s law. If q1 and q2 have the same sign as in Figure (3.5a), the product q1q2 is positive and the electric force on one particle is directed away from the other particle. If q1 and q2 are of opposite sign as shown in Figure (3.5b), the product q1q2 is negative and the electric force on one particle is directed toward the other particle. These signs describe the relative direction of the force but not the absolute direction. A negative product indicates an attractive force, and a positive product indicates a repulsive force. The absolute direction of the force on a charge depends on the location of the other charge. Fig. (3.5): Two point charges separated by a distance r exert a force on each other that is given by Coulomb’s law. The force F21 exerted by q2 on q1 is equal in magnitude and opposite in direction to the force F21 exerted by q1 on q2. 3.4 Electric field Let us consider a point charge Q placed in vacuum, at the origin O. If we place another point charge q0 at a point P, where OP = r, then the charge Q will exert a force on q0 as per Coulomb’s law. We may ask the question: If charge q is removed, then what is left in the surrounding? Is there nothing? If there is nothing at the point P, then how does a force act when we place the charge q at P. In order to answer such questions, the early scientists introduced the concept of field. According to this, we say that the charge Q produces an electric field everywhere in the surrounding. When another charge q0 is brought at some point P, the field there acts on it and produces a force. The electric field produced by the charge Q at a point r is given as: 𝑭𝒆 E= (3.2) 𝒒𝟎 We define the electric field due to the source charge at the location of the test charge to be the electric force on the test charge per unit charge, or, to be more specific, the electric field vector at a point in space is defined as the electric force acting on a positive test charge placed at that point divided by the test charge: The charge Q, which is producing the electric field, is called a source charge and the charge q0, which tests the effect of a source charge, is called a test charge. Note that the source charge Q must remain at its original location. However, if a charge q0 is brought at any point around Q, Q itself is bound to experience an electrical force due to q0 and will tend to move. The electric field E has the SI units of newtons per coulomb (N/C). The direction of electric field E is the direction of the force a positive test charge experiences when placed in the field, note that the existence of an electric field is a property of its source; the presence of the test charge is not necessary for the field to exist. The test charge serves as a detector of the electric field: an electric field exists at a point if a test charge at that point experiences an electric force. To determine the direction of an electric field, consider a point charge q as a source charge. This charge creates an electric field at all points in space surrounding it. A test charge q0 is placed at point P, a distance r from the source charge, as in Figure (3.6). We imagine using the test charge to determine the direction of the electric force and therefore that of the electric field.  For a positive charge, the electric field will be directed radially outwards from the charge. On the other hand, if the source charge is negative, the electric field, at each point, points radially inwards. Fig. (3.6): When a test charge q0 is placed near a source charge q, the test charge experiences a force and at a point P near a source charge q, there exists an electric field. 3.5 Electric Field Lines We have defined the electric field in the mathematical representation with Equation (3.2). Let’s now explore a means of visualizing the electric field in a pictorial representation. A convenient way of visualizing electric field patterns is to draw lines, called electric field lines and first introduced by Faraday, that are related to the electric field in a region of space in the following manner: The electric field E is tangent to the electric field line at each point. The line has a direction, indicated by an arrowhead that is the same as that of the electric field vector. The direction of the line is that of the force on a positive charge placed in the field according to the particle in a field model. The number of lines per unit area through a surface perpendicular to the lines is proportional to the magnitude of the electric field in that region. Therefore, the field lines are close together where the electric field is strong and far apart where the field is weak. Fig. (3.7): Electric field lines penetrating two surfaces.  These properties are illustrated in Figure (3.7). The density of field lines through surface A is greater than the density of lines through surface B. Therefore, the magnitude of the electric field is larger on surface A than on surface B. Furthermore, because the lines at different locations point in different directions, the field is non-uniform. Representative electric field lines for the field due to a single positive point charge are shown in Figure (3.8a). This two-dimensional drawing shows only the field lines that lie in the plane containing the point charge. The lines are actually directed radially outward from the charge in all directions. Because a positive charge placed in this field would be repelled by the positive source charge, the lines are directed radially away from the source charge. The electric field lines representing the field due to a single negative point charge are directed toward the charge (Fig. 3.8b). In either case, the lines are along the radial direction and extend all the way to infinity. Notice that the lines become closer together as they approach the charge, indicating that the strength of the field increases as we move toward the source charge. The rules for drawing electric field lines are as follows:  The lines must begin on a positive charge and terminate on a negative charge. In the case of an excess of one type of charge, some lines will begin or end infinitely far away.  The number of lines drawn leaving a positive charge or approaching a negative charge is proportional to the magnitude of the charge.  No two field lines can cross. Fig. (3.8): The electric field lines for a point charge.