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Electric Forces and Electric Fields Electrics Section 1 Objectives: Understand the basic properties of electric charge. Differentiate between conductors and insulators. Distinguish between charging by contact, charging by induction, and charging by polarization. Properties of Electric Charge: Like charges repel, unlike charges attract. Two types of electric charge: (named by Benjamin Franklin) Positive Negative These charges are opposite one another. Protons and neutrons are relatively fixed in the nucleus of the atom, but electrons are easily transferred from one atom to another. Ions-atoms with a negative or positive charge. Charge has a natural tendency to be transferred between unlike materials. What would happen if you rubbed two materials together? The area of contact would increase and the charge-transfer process would be enhanced. Application: If you rub a balloon against your hair, some of the electrons of your hair will transfer to the balloon. Your hair will become more _________, and the balloon will become more _________. *Only a small portion of the total available charge is transferred from one object to another. Since the positive charge on your hair is equal in magnitude to the negative charge on the balloon, electric charge is conserved in the process. Experiment: In 1909, Robert A. Millikan performed his oil-droplet experiment. Because of this experiment, he found that when an object is charged, its charge is always a multiple of a fundamental unit of charge, e. Charge is said to be quantized. Value of e: 1.602176 x 10-19C, where C (coulomb) is the SI unit of electric charge. Transfer of Electric Charge: Once materials such as Copper, zinc, and silver are charged in a small region, the charge readily distributes itself over the surface of the entire material (unlike the balloon/hair situation). Substances are classified by their ability to transfer electric charge. Electrical conductors-materials in which electric charge moves freely such as metals. Electrical insulators-materials in which electric charges do not move freely (e.g. glass, rubber, silk, plastic). Conductors: Semiconductors-a class of materials with electrical properties somewhere between those of insulators and conductors; insulators in their pure state, however, carefully controlled addition of specific atoms as impurities can dramatically increase ability to conduct electric charge. Silicon and Germanium are semiconductors utilized in many electronic devices. Superconductors-class of materials that can conduct electric current indefinitely without heating; have zero electrical resistance at or below a certain temperature (e.g. certain metals and compounds). Conductors: Insulators and conductors can be charged by contact. E.g. balloon/hair situation. Conductors can be charged via induction. Once a conductor is connected to Earth via a conducting wire or copper pipe, it is said to be grounded. Induction-the process of charging a conductor by bringing it near another charged object and grounding the conductor. Situation: A charged rubber rod brought near a metal sphere and the charge on the sphere is redistributed. If it is grounded, some of the electrons travel to the wire through the ground. As wire is removed, the sphere has an excess of positive charge. Electrons redistribute evenly on surface of sphere as rod is removed. A surface charge can be induced on insulators by polarization. When an object becomes polarized, it has no net chare but can attract or repel objects due to a realignment charge. So, a plastic comb can attract small pieces of paper with no net charge. As with induction, in polarization one object induces a charge on the surface of another object with no physical contact. Section 2 Objectives: Calculate the electric force using Coulomb’s law. Compare electric force with gravitational force. Coulomb’s law: Charles Coulomb found that the electric force between two charges is proportional to the product of the two charges. He also found that the electric force is inversely proportional to the square of the distance between the charges. Felectric=kCq1/q2, kC= Coulomb’s constant Force is a vector quantity. Sample Problem A: The electron and proton of a hydrogen atom are separated on average by a distance of about 5.3 x 1011m. Find the magnitude of the electric force and the gravitational force that each particle exerts on the other. Knowns: r= kC= me= mp= qe= q p= G= Electric force and Fgrav: The electric force between two objects always acts along the line that connects their centers of charge. Coulomb’s law applies to only point charges or particles and to spherical distributions of charge. Electric force is a field force as is gravitational force. Coulomb quantified electric force with a torsion balance. A torsion balance consists of two small spheres fixed to the ends of a light horizontal rod. In his experiment… One sphere is given a charge and another charged object is brought near the charged sphere. The attractive or repulsive force between the two causes rotation and twisting of the suspension by the rod. Section Objectives Calculate electric field strength. Draw and interpret electric field lines. Identify the four properties associated with a conductor in electrostatic equilibrium. The Electric Field Field forces, unlike contact forces, are capable of acting through space, producing an effect even when there is no physical contact between the objects involved. Electric field-a region where an electric force on a test charge can be detected. E, electric field=Felec/qo (a location) The SI unit of E=newtons per coulomb (N/C) What type of quantity is electric field? Electric field strength depends on charge and distance. Re-arrangement of Coulomb’s law If q is positive, the field due to this charge is directed outward radially from q. If q is neg., the field is directed towards q. Electric field lines: What do physicists use to assist in visualizing electric field patterns? Lines drawn and pointing in the direction of the electric field called electric field lines. These lines really do not exist. They are generally drawn so that the electric field vector, E, is tangent to the lines at each point. E is stronger where the field lines are close together and weaker where they are far apart. Rules for drawing electric field lines: 1. The lines must begin on positive charges or at infinity and must terminate on negative charges or at infinity. 2. The number of lines drawn leaving a positive charge or approaching a negative charge is proportional to the magnitude of the charge. 3. No two field lines from the same field can cross each other. Conductors in electrostatic equilibrium: Electrostatic equilibrium occurs when no net motion of charge is occurring within a conductor. Good electrical conductors (e.g. copper) contain charges (e’s) that are only weakly bound to the atoms in the material and are free to move about within the material. Characteristics of conductors in electrostatic equilibrium: The electric field is zero everywhere inside the conductor. Any excess charge on an isolated conductor resides entirely on the conductor’s outer surface. The electric field just outside a charged conductor is perpendicular to the conductor’s surface. On an irregularly shaped conductor, charge tends to accumulate where the radius of radius of curvature of the surface s smallest, that is at sharp points. Electric Potential Electric potential energy-potential energy associated with a charge due to its position in an electric field. Mechanical energy is conserved in the absence of friction and radiation. Electric potential energy is a component of mechanical energy. If a gravitational force, an elastic force, and an electric force are all acting on an object, the ME can be written as follows: ME= KE + PEgrav + PEeleastic + PEelectric Whenever a charge moves, because of the electric field produced by another charge or group of charges, work is done on that charge. Electric potential energy Electric potential energy can be associated with a charge in a uniform field: ∆PEelec = -qEd The negative sign indicates that the electrical PE will increase if the charge is negative and decrease if the charge is positive. Electric PE is similar to gravitational PE. At any point in an electric field, as the magnitude of the charge increases, the magnitude of the associated electrical PE increases. Electric potential-the work that must be performed against electric forces to move a charge from a reference point to the point in question, divided by the charge: V=PEelec/q The SI unit of potential difference and electric potential is the volt, V. The volt equals one joule per coulomb. The electric potential at a point is independent of the charge at that point. Potential difference is a change in electric potential. ∆V = ∆PEelec/q Daily application: batteries. For a typical battery, there is a potential difference of 13.2-V between the negative and positive terminals. The potential difference in a uniform field varies with the displacement from a reference point. PEelec = -qEd, ∆V = ∆(-qEd)/q Sample Problem A: A charge moves a distance of 2.0-cm in the direction of a uniform electric field whose magnitude is 215-N/C. As the charge moves, its electrical PE decreases by 6.9 x 10-19J. Find the charge on the moving particle. What is the potential difference between the two locations? ∆PEelec = ? d=? E=? q=? ∆V=? Solve the problem. Capacitance Capacitor-a device that is used to store electrical potential energy. Used in tuning the frequency of radio receivers, eliminating sparking in automobile ignition systems, and storing energy in electronics flash units. A charged capacitor is useful because energy can be reclaimed from the capacitor when needed for a specific application. A typical design for a capacitor consists of two parallel metal plates separated by a small distance. Capacitance-the ability of a conductor to store energy in the form of electrically separate charges. It is the ratio of charge to potential difference. Measuring Capacitance: The SI unit for capacitance is the farad, F, which is equivalent to a Coulomb per volt (C/V). Most capacitors have capacitancies ranging from microfarads to picofarads. Capacitance= C =Q/∆V What does capacitance depend on? The size and shape of the capacitor Capacitance for a parallel-plate capacitor in a vacuum: C=εo A/d=permittivity of a vacuum x area of one of plates/distance between the plates ε-epsilon denotes permittivity of the medium. When followed by a zero, it refers to a vacuum. The magnitudeis 8.85 x 10-12C2/Nxm2. Q=εOA/d ∆V for spheres, ∆V=kC Q/R; Csphere=Q/∆V=R/kC Capacitances: Earth has an extremely large capacitance because it is so large. Earth can provide or accept a large amount of charge without its electric potential changing too much. This is why Earth is used as a reference point for measuring potential differences in electric circuits. The material between a capacitor’s plates can change its capacitance. Discharging a capacitor releases its charge. Most capacitors are filled with a dielectric, an insulating material like air, rubber, glass, or waxed paper. The dielectric tend to increase capacitance. Energy and Capacitors: A charged capacitor stores electrical PE because it requires work to move charges through a circuit to the opposite plates of a capacitor. Electrical potential energy stored in a charged capacitor: PEelec=1/2 Q∆V PEelec=1/2 C(∆V)2; PE=Q2/2C Sample Problem B: A capacitor, connected to a 12-V battery, holds 36µC of charge on each plate. What is the capacitance of the capacitor? How much electrical PE is stored in the capacitor? List Knowns: List Unknowns: Solve: Electrical Current: Current-the movement of electric charge through a medium. What types of things are powered by electric currents? Lights, radios, TV's, air conditioners, and refrigerators, automobiles. Electrical current is a part of the human body. Luigi Galvani: What connection did Galvani make between physics and biology? Internet. Electric current-the rate at which electric charges pass through a given area. Variables and Equations: ∆Q=amount of charge passing through the area ∆t=time interval I=current, ratio of amount of charge to the time interval. I=∆Q/∆t The SI unit of charge is the ampere, A. One ampere is equivalent to one coulomb of charge passing through a cross-sectional area in a time interval of one second (1A=1C/s). Sample Problem C: The current in a light bulb is 0.835-A. How long does it take for a total charge of 1.67-C to pass through the filament of the bulb? I=0.835-A Q=1.67-C t=? Current and Voltage: V=IR, I=V/R Resistance-the opposition to the motion of charge through a conductor; the opposition presented to electric current by a material or device. R=∆V/I The SI unit for resistance is the Ohm or 1V/A. Ohm’s Law: Resistance is constant over a range of potential difference. Georg Simon Ohm was 1st to study electrical resistance in a systematic manner. This law does not hold for all materials. Resistance What does resistance depend on? Length, area, material, and temperature. What is used to control the amount of current in a conductor? Resistors Resistor-a simple electrical element that provides a specified resistance. What lowers the body’s resistance? Salt and water perspiration. The human body has a high resistance to current when the skin is dry. Potentiometer-a special type of resistor with a fixed contact on one end and an adjustable, sliding contact that allows the user to tap off different potential differences. Sample Problem D: The resistance of a steam iron is 19.0-Ω. What is the current in the iron when it is connected across a potential difference of 120-V? V=120-V R=19-Ω Electric Power: Batteries and generators supply energy to charge carriers. Batteries convert chemical energy to electrical PE. Generators are preferred over batteries because batteries need recharging or replacing. Generators convert ME into electrical energy. Generators are the source of electric current to a wall outlet in a home and supply the electrical energy to operate appliances. Current can be direct or alternating. Direct current is unidirectional and negative charges move from low to higher electrical potential. E.g. batteries. With alternating current, the terminals of the source of potential difference are constantly changing sign. Power Electric power- the rate at which charge carriers do work. P=W/t=∆PE/∆t, P=I∆V, ∆V=∆PE/q P=I∆V=∆V/R(∆V)=(∆V)2/R, P=VI, P=I2R Sample Problem E: An electric space heater is connected across a 120-V outlet. The heater dissipates 1320-W of power in the form of electromagnetic radiation and heat. Calculate the resistance of the heater. V=IR, I=P/V Circuits and Circuit Elements: Schematic diagram-a diagram that depicts the construction of an electrical apparatus. Electric circuit-a set of electrical components connected such that they provide one or more complete paths for the movement of charges. Any element or group of elements in a circuit that dissipates energy is a load. www.worldofteaching.com Sample Problem A: A 9.0-V battery is connected to four light bulbs, find the equivalent resistance for the circuit and the current in the circuit. List Knowns: List Unknown: Solve: