Chapter 16: Electric Forces and Fields1 Section 1: Electric Charge Properties of charge Have you ever noticed: Static cling Rubbing your feet against the carpet and then touching a door knob or light switch Fly-away hair after combing These experiences are the result of electrical charges. 2 kinds of electric charge o Positive charge o Negative charge Like charges repel Unlike charges attract o Ex. Electrostatic painting negatively charged paint droplets are attracted to the positively charged target object (less wasted paint) Electric charge is conserved Remember your chemistry … Parts of the atom: Protons (+ charge) Neutrons (no charge; neutral) o Nucleus (center of the atom) Electrons (― charge) o Outside the nucleus; in motion o Easily transferred When protons = electrons, no net charge If an electron is transferred from a neutral atom to another, both atoms have acquired a charge o Lose an electron, + charge o Gain an electron, ― charge o Both are now called ions Charge has a natural tendency to be transferred between unlike materials. Rubbing the materials together increases the area of contact Enhances the charge-transfer process Only a small portion of the total available charge is transferred from one object to another Charge transferred to a second object = the charge “lost” by the first object o + charge is equal in magnitude to ― charge Principle of Conservation of charge Electric charge is conserved; no charge is created or destroyed. Fundamental laws of nature Chapter 16: Electric Forces and Fields2 Electric force is quantized Transferring electric charge Robert Millikan’s oil-drop experiment When charged by rubbing, the charge does not move into other regions of the material. When some materials (like copper, aluminum, silver) become charged in one small area, the charge distributes itself over the entire surface of the material. Demonstrated that when an object is charged, its charge is always a multiple of a fundamental unit of charge, represented by e. o + e, +2e, +3e, etc. o Electrons have a charge of –e o Protons have the charge of +e o Value of e = 1.60 x 10-19C o C = coulomb, the SI unit of charge o -1 C (as in 1 C of electrons) contains 6.2 x 1018 electrons Charging by contact Charging by contact – materials become charged when rubbed together Insulators can be charged by contact Like charges repel Unlike charges attract Conductors can be charged by contact if you hold a metal with an insulated material and then rub it. Without the insulator, the charges that are produced by rubbing move through the metal, then through your body (also a conductor), and ends up in the Earth (going to ground or being grounded). The Earth is considered to be an infinite reservoir for electrons because it can accept an unlimited amount of electrons. Classify materials based on their ability to transfer electric charge Electrical conductors: materials in which electric charges move freely o Metals Electrical insulators: materials in which electric charges do not move freely o Glass, rubber, silk, plastic Semiconductors: electric properties are somewhere between conductors and insulators o Pure state – insulators o When specific materials are added as impurities, become conductors Superconductors have zero electrical resistance when they are at or below a certain temperature o Can conduct electricity indefinitely without heating up Charging by induction When a charged rod is brought near a neutral (uncharged) sphere, the electrons in the charged rod repel the electrons in the sphere, causing the charge in the sphere to be redistributed. Region nearest to the rod now has an excess of positive charge Induction: process of charging a conductor by bringing it near another charged object while the conductor is grounded. Chapter 16: Electric Forces and Fields3 Polarization Process similar to charging by induction Works on insulators In the presence of a charged object, positive charge shifts slightly away from the negative charge – resulting in a more positive charge on one side and a more negative charge on the other (polarization) Insulator has no net charge, but is still able to attract or repel objects due to realignment. Section 2: Electric Force Coulomb’s Law Electric force: the force that two charged objects exert on each other, causing an acceleration either toward or away from each other The closer the two charges are, the greater the force Amount of charge on the objects affects the magnitude of the electric force There is a relationship between distance, charge, and electric force Coulomb’s law: Force is a vector quantity Electric force = Coulomb constant x (charge 1)(charge 2) (distance)2 Felectric = kC(q1q2) r2 9 kC = Coulomb constant = 8.99 x10 N•m C2 2 Force between 2 objects always acts along the line that connects their centers of charge Coulomb’s law applies only to point charges or particles, and to spherical distributions of charge. o r = distance between centers of the spheres Chapter 16: Electric Forces and Fields4 Practice 16A The electron and proton of a hydrogen atom are separated, on average, by a distance of about 5.3 x 10-11 m. Find the magnitudes of the electric force and the gravitational force that each particle exerts on the other. What you need to know, but may not remember (or know where to find the info): me = 9.109 x 10-31 kg mp = 1.673 x 10-27 kg Conceptual question Consider two forces, F1 = F and F2 = ―F acting on two charged particles separated by a distance, d. Explain the change in forces under these conditions: Distance between the 2 particles doubles Charge on one particle doubles Charge on both particles doubles Charge on both particles doubles, distance between the particles also doubles G = 6.673 x 10-11 N•m2/kg2 Resultant force on a charge is a vector sum of the individual forces on that charge Coulomb’s law gives the electric force between any pair of charges. Still applies when there are more than two charges present Resultant force on any single charge is the vector sum of the individual forces exerted on that charge by all of the other individual charges present. o Called principle of superposition o Find the magnitudes of the individual electric forces o Add the magnitudes as we did earlier Straight line – add/subtract Not in a line, but right angles, Pythagorean theorem Not in a line, not 90°, components and Pythagorean theorem Chapter 16: Electric Forces and Fields5 Practice 16B Consider three point charges at the corners of a triangle, as shown below, where q1 = 6.00 x 10-9C, q2 = -2.00 x 10-9C, and q3 = 5.00 x 10-9C. Find the magnitude and direction of the resultant force on q3. An object in equilibrium Net external force acting on a body in equilibrium must be zero. Equilibrium position of a charge is the location where the net electric force on the charge is zero. To find this position: Find the position where the electric force from 1 charge is equal and opposite the electric force from another charge. Set the forces (found by Coulomb’s law) equal to each other and then solving for the distance between either charge and the equilibrium position. Chapter 16: Electric Forces and Fields6 Practice 16C Three charges lie along the x-axis. One positive charge, q1 = 15 μC, is at x = 2.0 m, and another positive charge, q2 = 6.0 μC, is at the origin. At what point on the x-axis must a negative charge, q3, be placed so that the resultant force on it is zero? Electric force is a field force Field force: a force that is exerted by one object on another without physical contact Gravitational force is another example Electrical forces: Can be attractive or repulsive o Gravity is only attractive Electrical force is MUCH stronger than gravitational force o Only a small amount of charge is required to overcome the gravitational force (balloon on hair trick) Chapter 16: Electric Forces and Fields7 Section 3: The Electric Field Electric Field Strength Electric Field: No physical contact between objects required Acts through space Set up by a charged object in the space around it o Second charged object enters the field of the first charged object, and interacts with the electric field Electric field strength is defined as the magnitude of the electric force acting on a small, positively charged particle (q0) that enters the field of a much larger positive charge. E = Felectric q0 units are the ratio of force to charge, so N/C (newtons per coulomb) Vector Direction of E (electric field) is defined as the direction of the electric force that would be exerted on a small positive charge (test charge) o Direction of E depends on the sign of the charge producing the field Electric field strength depends on charge and distance To find the electric field strength from a point charge, consider a small test charge, q0, located a distance, r, from charge q. Coulomb’s law: Felectric = kCqq0 r2 Combine this value for Felectric in the Electric field strength equation: E = Felectric = kCqq0 q0 r2q0 E is a vector E = kCq r2 If q is positive, the field due to q radiates outward If q is negative, the field is directed toward q Electric field due to more than one charge is calculated by using the principle of superposition. Depends only on the charge, q, setting up the field, and the distance, r, from that object to a specific point in space. Electric field = Coulomb con. x charge producing field strength (distance)2 Chapter 16: Electric Forces and Fields8 Practice 16D A charge q1 = +7.00 µC is at the origin, and a charge q2 = -5.00 µC is on the x-axis 0.300 m from the origin. Find the electric field strength at point P, which is on the y-axis 0.400 m from the origin. Chapter 16: Electric Forces and Fields9 Electric field lines Electric field lines drawn in the direction of the electric field are a convenient aid for visualizing electric field patterns. Electric field lines are NOT physical lines – they do not physically exist Field lines are a visual representation of the field that would be experienced by a positive test charge Cannot be observed directly; only the effects of the field can be observed. Represent both the strength and the direction of the field at different points in space. Field lines make it easier to visualize the net field at each point when the field is the result of more than one charge. How to draw electric field lines Number of lines is proportional to the strength of the electric field Closer the lines, the stronger the field; the farther apart the field lines, the weaker the electric field Drawing is two-dimensional, but reality is three-dimensional (like porcupine quills) No two field lines can cross each other o At every point in space, the electric field vector points in a single direction and any field line at that point also points in the same direction. o Positive charge: electric field lines radiate outward because a positive test charge would be repelled; the lines are directed away from the positive charge toward infinity o Negative charge: electric field lines are directed inward toward the charge Lines are closer together as the lines get nearer the charge, indicating that the field strength is increasing Field strength equation is inversely proportional to distance squared 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. Chapter 16: Electric Forces and Fields10 Electric dipole 2 equal and opposite point charges Number of lines that begin on the positive charge must equal the number of lines that terminate on the negative charge Points very near the charges are nearly radial High density of lines between the charges indicate a strong electric field Unequal, opposite charges Positive charge is twice the magnitude of the negative charge Number of field lines leaving +2q is twice the number of field lines terminating on –q. The other field lines terminate at infinity. At great distances, the electric field pattern equals that of a single charge, +q. Two equal positive charges Close to either charge, the lines are nearly radial Same number of lines emerges from each charge (equal in magnitude) At great distances from the charges, the electric field equals that of a single change of magnitude 2q.