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charge acquired by the glass rod when it is rubbed with silk is positive, since it gains an excess of protons. The charge acquired by the silk cloth, on the other hand, is negative. — W Overall charge negative Overall charge positive silk glass rod Transfer of Electric Charge You usually notice that after brushing a plastic comb through your hair on a dry day, the comb attracts strands of your hair. This happens because your hair and the comb become electrically charged through rubbing. Electric charges on the rubbed plastic comb make the hair behave in an unusual way. What does it mean when we say that the plastic comb is charged through rubbing? Rubbing two different kinds of materials against each other may cause the transfer of electrons from one material to another. This upsets the balance between the positive and negative charges. When rubbed, some objects lose charge almost as soon as they gain it. This happens because electrons flow through the object or surrounding materials until the balance of negative and positive charge is restored. Consider the case of the polythene and Perspex combs and the hair rubbed together. A B + polythene comb + Perspex comb hair hair When a polythene comb is pulled through hair, the polythene pulls electrons from atoms in the hair. This leaves the polythene with more electrons than normal and the hair with less. The polythene becomes negatively charged. However, when a Perspex comb is pulled through the hair, the hair pulls the electrons from the Perspex and the hair becomes negatively charged while the Perspex comb becomes positively charged. When the weather is cool and dry, it is easy to charge an object. You can rub an inflated balloon back and forth across your hair and find that the balloon is attracted to your hair.; you can even stick the balloon to the wall afterward. As you rub an inflated balloon back and forth across your hair, you give the balloon an electric charge. Rubbing transfers electrons from the hair to the balloon. The balloon becomes negatively charged because of its extra electrons. If you hold the balloon up to a wall, the balloon sticks to it. The negatively charged balloon is attracted to the positive charges in the wall. However, if you rub two balloons next to each other, they push each other apart. These attraction and repulsion follow the law of electric charges that states that like charges repel and unlike charges attract. The presence of excess electric charge can be detected by an electroscope. An electroscope consists of a metal rod with a knob at the top. At the bottom of the rod are two sheets or leaves of very thin metal (aluminum, silver or gold). When the electroscope is uncharged, the leaves hang straight down. When the knob is charged, electric charge travels along the rod and into the leaves. Then, the leaves repel each other because they have the same charge. one-hole rubber stopper flask. knob metal rod Uncharged electroscope negatively charged plastic rod metal leaves electrons repelled Charged electroscope electrons attracted X X XXXX Charged electroscope positively charged glass rod Electric charges are more easily moved in some materials. This characteristic led to the classification of materials into two groups – conductors and insulators. Materials whose electric charges are free to move within are called conductors. Examples of conductors include copper, aluminum, silver, iron, carbon and water, In some materials, electric charges are not free to move within. Such materials are called insulators. Insulators include glass, rubber, silk and plastic. Another kind of material that is somewhere between insulators and conductors, such a silicon and germanium, is called a semiconductor. Certain materials known as superconductors become perfect conductors at very low temperatures. Currently, the material that exhibits superconductivity at the highest temperature is a type of ceramic copper oxide that is effective below 139 K (-134 °C). A (B) movement of electrons Charging by conduction such as this involves direct contact between the charged rod or cloth and the sphere. + neutral charge charged object becomes negatively charged B negative charges in the rod repel negative charges in the spheres insulator induced charges xxx becomes positively charged B + when the spheres are separated, each one is charged movement of electrons B removing the charged rod leaves two charged spheres The charged comb induces charges on the small bits of paper which are said to be polarized. Conductors can be charged by conduction. Conduction is the transfer of electrons from a charged object to another object by direct contact. In the conduction process, a body with one type of charge produces the same type of charge on a conductor. A conductor can also be charged by induction. Induction is the movement of electrons to one part of an object by the electric field of another object. In the induction process, the opposite type of charge is produced. However, even in an insulator, the electric charges can shift slightly to one side when there is a charge nearby; this effect is called polarization. A (B) movement of electrons Charging by conduction such as this involves direct contact between the charged rod or cloth and the sphere. + neutral charge charged object becomes negatively charged B negative charges in the rod repel negative charges in the spheres insulator induced charges xxx becomes positively charged B + when the spheres are separated, each one is charged movement of electrons B removing the charged rod leaves two charged spheres The charged comb induces charges on the small bits of paper which are said to be polarized. Electrostatic charging can be dangerous, but it can also be beneficial in a variety of practical applications. Paper and clothes often stick together because of static cling, and an electrostatic spark discharge can start a fire or cause an explosion in the presence of a flammable gas. On the other hand, some practical applications of electrostatic charging include the electrostatic dust precipitators, attracting droplets of sprayed paint to a car body and attracting toner particles to charged regions of the imaging drum in a copying machine. DID YOU KNOW? Lightning is caused when a large electric charge builds up on a cloud as the result of ice and water particles the cloud rubbing together. Positive charges build up at the bottom. The electrons suddenly leap from the cloud to the ground or to another cloud. When you walk across some types of nylon carpet, static electricity builds up on you. If you touch something metallic, small sparks will jump from you to the metal. When you take off a nylon shirt or blouse, you can some- times hear a crackling sound and see small sparks. These sparks are like miniature lightning flashes. COULOMB'S LAW About three centuries ago, a French scientist, Charles-Augustin de Coulomb, conducted the first quantitative work with electric charges. He studied the magnitude and the direction of the force between two charged spheres in relation to the magnitude of the charges and the distance between them. He measured the small forces involved with the very small charges he obtained by using a method similar to the one used by Henry Cavendish in calculating the value of the gravitational constant G. Coulomb was able to show that the force F between two charged spheres was inversely proportional to the square of the distance R between their centers. In symbols, Fa Fα = 2²² 1 Coulomb was also able to establish the direct relationship of F to the charges Q₁ and Q₂, keeping R between them constant. In symbols, F & Q₁ and F x Q₂. а Combining the given relationship of F to Q1, Q2 and R we have: F α Q 1 Q ₂ R² 2 Introducing a constant of proportionality k, this becomes: F = k ²19₂ R² The above equation that relates the electric force with the two charges and the distance between them is known today as Coulomb's law. This law states that the force of attraction or repulsion between two small charged bodies is directly proportional to the product of the two charges and inversely proportional to the square of the distance between them. + 1-2 R 2-1 Q₁ Q₂ R² F = k- 1-2 F2-1 = -K Q₁ Q₂ R² Q₂ N N + F₁₂ Q₁ 1-2 R (1010 1-2 PAJESTY F₁₂ - KQ²N k- F2-1=kQ₁ Q₂ R² 00 Q₂ N tha 2-1 The standard unit for charge is called coulomb, C, in honor of Charles-Augustin de Coulomb. It is defined in terms of some properties of moving charges. One coulomb is defined as the amount of charge transferred through a point on a conductor in one second by a current of one ampere. Hence, we represent charge by the relation: Q = It Q - charge in coulombs I – current in amperes t - time in seconds After the unit of charge was ascertained, the constant of proportionality k was measured. Experimental results in a vacuum placed k at a value very close to 9 x 10º N•m²/C². where Sample Problem 1 What is the magnitude and direction of the force on a charge +4 x 10-⁹ C that is 5 cm from a charge of +5 x 10-8 C? Given: Q₁ = +4 x 10-⁹ C Q₂ = +5 x 10-8 C R = 5 cm = 5 x 10-² m Required: F Solution: F = k²¹⁹² = (9 x 10º N•m²/C²)- +4 x 10−9 C)(+5 x 10-8 C ) 1 R² (5 x 10-2 m)² 2 1.8 x 10-6 N ●m² 2.5 x 10-3 m² F = 7.2 x 10-4 N The force is directed away from the +5 x 10-8 C charge since both charges are positive. Sample Problem 2 Two identical charges repel each other with a force of 10-5 N when they are 20 cm apart. (a) What is the force on each when they are 5 cm apart? (b) When they are 100 cm apart? (a) 1.6 x 10-4 N (b) 4 x 10-7 N ELECTRIC FIELDS B.1 Nature and Characteristics of Electric Field Whenever you have a charge placed anywhere in Q space, it will be surrounded by a region such that if you will put any other charge q at any oint P in this region, the charge q will be acted upon by an electric force Fe. We call this region around Q the electric field E of Q. The strength of this electric field is operationally defined as the ratio of the electric force F to the charge a placed at that point in the field. In symbols, E = Fe q What will be the electric field direction if Qis positive? If you put a positive test charge +q (a test charge is always taken as small, positive charge) at any point in the electric field, it will be repelled by the center charge, +Q. An electric force F now acts on the test charge +q. The electric field direction follows the direction of this electric force F acting on the positive test charge. +Q A +q electric field lines or lines of force around a positive charge Q ALL +q * ALL electric field lines or lines of force around a negative charge Q B Since test charge are always positive, then the electric field of a positive charge +Q will always be directed away from the center. What happens if Q is negative? If you put a test charge at any point in the electric field of -Q, the test charge +q will be attracted toward –Q. The force vector Fe acting on +q is then directed toward the center charge, -Q. Since the direction of the electric field E always follows the direction of the force vector Fe on a test charge, the direction of the E of a negative center charge is always to the center. Sample Problem What is the electric field strength at a point 30 cm from a charge q = 4 x 10¹⁹ C? R = 30 cm q= 4 x 10⁹ C ESA: From Coulomb's law, the force on a test charge q' 30 cm from q has magnitude G: Fe = kqq'/R² = (9 x 10⁹ Nm²/C²)(4 x 10-⁹ C) (q)/(0.3 m)² Fe = (400 N/C) (q) F Then from the equation E = F -e = q Required: E > q = 400 N/C the magnitude of E is E The direction of E at this point is along the line joining q and q', away from q. B.2 Electric Lines of Force After discussing the direction of the electric force of a single charge Q, what do you think would be the direction of the electric field when two point charges are present? A +Q₁0 (B) d₁ P +q tu F d₂ -Q₂ -Q₂ C +Q₁ +Q₁ +q to nomrop F F₂ F₂ F₁ Fo net -Q₂ net = F₁+F₂ -Q₂ Suppose you are asked to evaluate the direction of the electric field at point P. As in the cas of single charges, we will evaluate the direction in the presence of two charges by evaluating first the direction of the force F that will act on a positive test charge placed at point P. Look at letter B. For simplicity, let us assume that d1 is equal to d2. This means that the force F1 acting on +q due to +Q1, and the force F2 acting on +q due to −Q2 are of equal magnitudes. The force vector diagram can be represented as in the letter C. The net force Fn would then be directed to the right. Figure letter D shows the direction of the net force. The direction of the electric field at point P would then follow the direction of the net electric force acting on a test charge at the same point. The direction of the electric field depends on the direction of the bet electric force acting on a test charge. The process of determining these directions may actually be tedious. To simplify the process, scientists have agreed on the use of imaginary lines drawn in such a way that at any point on the line, the tangent to the line at that point will determine the direction of the electric field. The next picture shows a sample diagram of these imaginary lines. We call these imaginary lines the electric lines of force. A E +2Q E E +Q 3. -Q B D Note the tangents drawn at three points in the field in Letter A. generally, the electric field direction is away from +Q and is toward –Q. We have just discussed variations in the directions of the electric field E. What about its variations in magnitude? On what factors does the magnitude of the electric field depend? Analyze the equation for electric field strength expressed as E = F e q This is the electric field strength of a center charge Q, as expressed in terms of the force Fe, which another charge q will experience when placed at a point P in the field at a distance R from Q. Look at the next picture. The magnitude of the electric field strength at point P will then be the same as the equation for electric field strength. Notice that Fe is actually the electric force of interaction between the two charges, Q and q. +Q R P +q 1LLº ➜DID YOU KNOW? The intensity of the electric field in the atmosphere is high when a thunderstorm is approaching. This is the reason why, during bad weather, sailors in the old days often observed a natural corona found at the mast of their ship. They called this corona St. Elmo's fire, after St. Elmo-the patron saint of sailors in the Med- iterranean region. dignstla This means that while +Q is repelling +q with a force Fe, is also repelling +Q with a force equal in magnitude but opposite in direction to Fe. Recalling Coulomb's law, we can express the magnitude of Fe in terms of charges Q and q and the distance R between them. In symbols, we have: F = k R² Substituting the equation with the equation for electric field strength, we get: Qq E = k /q Qq R² Qq 1 R² q E = k- al E = k- R² In this equation, we have another expression for the magnitude of the electric field strength, this time in terms of the Coulomb's law constant k, the center charge Q, and the distance R between Q and the point P, at which the electric field strength is evaluated. Note that, at any measured distance R from a known charge Q, the electric field strength of Q can be known. This means therefore that the electric field strength E at any point is not dependent on the value of q that may be placed at the point. Sample Problem A test charge of +1 x 10-6 C is placed halfway between a charge of +5 x 10-6 ℃ and a charge of +3 x 10-6 C that are 20 cm apart. Find the magnitude and direction of the force on the test charge. Which exerts a greater force on q, Q1 or Q2? Why? Where will the net force of q be directed, to the left or to the right? Q₁ + ← F₂ q 20 cm F₁ Q₂ + H The force exerted on the test charge q by the charge Q1 is (9x109² Nm2 C2 _Q1q R² F1 = k −)(1x10–6 C)(5x10–6 C) (0.1 m)² This force is taken to be positive because it acts to the right. F2 = 1229 R² Q2q k = +4.5 N The force exerted by the charge Q2, on q is Nm2. (9x109- )(1x10-6 C)(3x10-6 C) C2 (0.1 m)² The net force on the test charge q is = -2.7 N This force is taken to be negative because it acts to the left. Fn = F1 + F2 = +4.5 N − 2.7 N = +1.8 N Fn acts to the right, that is, toward the +3 x 10-6 C charge.