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Welcome to Physics 152 ©Hyde-Wright, ODU © Walker, Prentice Hall, 2007 Topics to be covered • Electricity and Magnetism (Chapters 19-23) • Light and Optics (Chapters 25-28) • Modern Physics (Chapter 29-32) Walker, Chapter 19 2 Chapter 19 Electric Charges, Forces, and Fields Fundamental Forces in Physics • • • • Gravity Electromagnetism Weak Interaction Strong Interaction All of physics is based on these four forces Walker, Chapter 19 3 Energy in our World • Nuclear Fusion in sun E=mc2 H H H H He + n + n + Energy Thermal Energy at surface converted to visible light energy • Light Energy Chemical Energy (photosynthesis) • Plants Fossil Fuels Fusion Radiation Fuel for cars (motion) Fuel for power plants • Plants Food Energy for thought, motion of muscles, etc... Walker, Chapter 19 4 Electrostatic Phenomena • Rubbing things makes an electrostatic charge Walker, Chapter 19 5 Electrical Charge Effect of Electric charge have been known since ~600 B.C. Greeks experiment: amber rubbed against fur - charge (Greek word for amber is elektron.) Glass rubbed against paper towel + charge The SI unit of electrical charge is the Coulomb (C ). Walker, Chapter 19 6 The Structure of an Atom The atom consists of a positively charged nucleus, orbited by negatively charged electrons. The nucleus contains protons (positive) and neutrons (neutral). Walker, Chapter 19 7 The Electron One of the fundamental particles found in nature is the electron. • The electron mass is 9.11 10-31 kg. • The electron charge (-e) is -1.6 10-19 C. The symbol e is the magnitude of the electron’s charge Walker, Chapter 19 8 The Proton The proton is not a fundamental particle. The proton mass is 1.67 10-27 kg. • The proton is 2000 times heavier than the electron, so the vast majority of an atom’s mass resides in the nucleus. • The proton charge (+e) is +1.6 10-19 C. • The proton charge and electron charge are known to be equal and opposite. Walker, Chapter 19 9 • An object may contain both positive and negative charges. If the object possesses a net charge it is said to be charged. If the object possesses no net charge it is said to be neutral. • An atom is normally neutral, because it possesses an equal number of electrons and protons. However, if one or more electrons are removed from or added to an atom, an ion is formed, which is charged. • Charge is always conserved: charge may be transferred but it is never created or destroyed. However, charges can be created and destroyed in positive and negative pairs, so that the net charge in the universe does not change. Walker, Chapter 19 10 Electrical Forces Two charged objects will exert forces on one another. • Unlike charges attract one another. + • Like charges repel one another. + + • The force decreases with the square of the distance between the charges Walker, Chapter 19 11 Polarization An object is polarized when its charges are rearranged so that there is a net charge separation. Charged objects can be attracted to neutral objects because of polarization. charged Walker, Chapter 19 neutral & polarized 12 Insulators and Conductors Materials are classified by how easily charged particles can “flow” through them. • If charges flow freely, the material is a conductor (metals, for example) • If charges are unable to move freely, the material is an insulator (glass, for example) • Some materials have properties in between insulators and conductors, these are called semiconductors. Walker, Chapter 19 13 Charge Transfer Charge is usually transferred because electrons move from one place to another. But sometimes the flow of both positively or negatively charged ions (atoms or molecules) is important (cells, batteries…). The earth can be viewed as an infinite (conducting) reservoir of electrons. An object in electrical contact with the earth is said to be grounded. Walker, Chapter 19 14 Coulomb’s Law The magnitude of the force between two point objects separated by a distance r with charges q1 and q2 is given by Coulomb’s Law: F k q1q2 r 2 q1 and q2 are the values (+ or ) of the two charges where k = 8.99… 109 Nm2/C2 The direction of the force on one charge is either toward (negative) or away (positive) from the other charge. Walker, Chapter 19 15 Force: vector, magnitude, component | q1 || q2 | • Magnitude (strictly positive) | F | k 2 r Walker, Chapter 19 16 Force: vector, magnitude, component | q1 || q2 | | F | k r2 • Magnitude (strictly positive) F12 Force on charge q1 from charge q2 F21 Force on charge q2 from charge q1 F21 - F12 : Newton's Third Law: Action-Reaction q1 F12 F21 Walker, Chapter 19 + q2 17 Walker Problem 14, pg. 657 Given that q = +12 mC and d = 16 cm, (a) find the direction and magnitude of the net electrostatic force exerted on the point charge q2. (b) How would your answers to part (a) change if the distance d were tripled? Walker, Chapter 19 18 Walker, Chapter 19 19 b) Tripling the separations: Walker, Chapter 19 20 Multiple Charges • If there are more than two charges present, the net force on any one charge is given by the vector sum of the forces on that charge from all surrounding charges. This is an example of the Principle of Superposition. + + What is the direction of the net force on each charge (roughly)? Walker, Chapter 19 21 Walker Problem 20, pg. 658 Find the direction and magnitude of the net electrostatic force exerted on the point charge q2 in the Figure. Let q = +1.8 mC and d = 47 cm. Walker, Chapter 19 22 Walker, Chapter 19 23 Electric Field • If a test charge q0 experiences a force F at a given location r, the magnitude of the electric field at that location is defined by F E q0 • The electric field can also be thought of as a disturbance in space caused by nearby charges. • The electrostatic force experienced by a charge is the interaction between the charge and the electric field at that position. • The SI units of electric field are Newtons/Coulomb = N/C Walker, Chapter 19 24 Electric Force F(r) from charge Q acting on a test charge q0 at various locations r : F=kQq0/r2 Electric Field E(r)= F/ q0 q0 Q Walker, Chapter 19 25 Electric Field E(r) from charge Q at various locations r: E=kQ/r2 r Q Walker, Chapter 19 26 Electric Field Direction The direction of the electric field is defined to be the direction of the force that would be experienced if the test charge is positive. Because the field has a direction, it must be a vector. E q0 q0 E + Walker, Chapter 19 27 Electric Field (cont.) The electric field is the force per charge at a given location. If you know the electric field, then the force on a charge can easily be found using F = qE Example: A charge q of +8 mC experiences a uniform electric field of 1000 N/C to the right. (a) What is the force on the charge? (b) What would the force be if the charge were –8 mC? q Note: In problems like this we do not need to know what charges created the electric field. Walker, Chapter 19 E = 1000 N/C 28 Electric Field of a Point Charge From Coulomb’s Law, the magnitude of the force experienced by a test charge q0 a distance r from a charge q is qq F k r 0. 2 Since the definition of the electric field is F E , q0 the magnitude of the electric field from a point charge is given by q Ek r . 2 Walker, Chapter 19 29 Walker Problem 28, pg. 642 What is the magnitude of the electric field produced by a charge of magnitude 10.0 mC at a distance of (a) 1.00 m and (b) 2.00 m? Q Ek 2 r k = 8.99 ·109 N m2/C2 Walker, Chapter 19 30 Superposition Just like with forces, electric fields must be added as vectors. The electric field from several charges is the vector sum of the electric field from each charge. Example: Consider two identical negative charges as shown. At which lettered point is the magnitude of the electric field greatest? Least? a b c Walker, Chapter 19 31 Walker Problem 76, pg. 661 An object of mass m = 3.7 g and charge q = +44 mC is attached to a string and placed in a uniform electric field that is inclined at an angle of 30.0° with the horizontal. The object is in static equilibrium when the string is horizontal. Find (a) the magnitude of the electric field and (b) the tension in the string. Walker, Chapter 19 32 Walker, Chapter 19 33 Electric Field Lines In order to visualize the electric field in space it is convenient to draw Electric field-lines (see Fig. 19-13). The field lines are directional [curved] lines that everywhere point in the direction of the electric field at that point. + + Dipole Walker, Chapter 19 34 Field Line Properties • The electric field is tangent to the field line at any point in space. • The strength of the electric field is proportional to the density of field lines. • The field lines always begin on positive charges or at infinity and end on negative charges or at infinity. • No two field lines can ever cross. • The number of field lines leaving a positive charge or approaching a negative charge is proportional to the magnitude of the charge. Walker, Chapter 19 35 Electric Field Lines Note that twice as many field lines originate from the +2q charge than the +q or –q charges. Walker, Chapter 19 36 1. The net charge inside the grey ellipse is: a) Positive b) Zero c) Negative Hint: Are there more Electric Field lines entering, or leaving the gray ellipse, or is it equal? Walker, Chapter 19 37 2. The net charge inside the grey ellipse is: a) Positive b) Zero c) Negative Hint: Are there more Electric Field lines entering, or leaving the gray ellipse, or is it equal? Walker, Chapter 19 38 Electrostatic Equilibrium Recall that charges within a conductor are free to move around easily. If the charges within a conductor are not in motion, then the system is said to be in electrostatic equilibrium. Walker, Chapter 19 39 Properties of Electrostatic Equilibrium • In the presence of electrostatic forces, the charges on the conductor move around until the following static conditions are achieved: The electric field is zero everywhere inside a conductor. The excess charge on a conductor resides entirely on its surfaces. The electric field just outside a charged conductor is perpendicular to its surface. • On irregularly shaped objects, the charge accumulates at sharp points, and the electric field is most intense at sharp points. Walker, Chapter 19 40 Electric Flux We define electric flux F as the product of the surface area A times the component Ecosq of the electric field perpendicular to the surface. In general, F = EAcosq. (a) F EA (b) F = 0 (c) F = EAcosq q is the angle between the electric field and the line perpendicular to the surface. Walker, Chapter 19 41 Gauss’s Law Consider an arbitrary (imaginary) closed surface (called a Gaussian surface) enclosing a total charge q. The electric flux through the surface is q F 0 0 41k 8.851012 C2 /N m2 This integral property is a consequence of the 1/r2 Coulomb Law, and is valid for any irregular surface, no matter how complicated the electric field produced by internal or external charges. Walker, Chapter 19 42 Example Three point charges are arranged as shown. q1 = +4 mC, q2 = -6 mC and q3 = -4 mC. Find the electric flux through the three Gaussian surfaces labeled a, b and c. a b q 1 c q3 q2 Walker, Chapter 19 43 • Two charges Q1 and Q2 are separated by a distance of 0.010 m. The Electrostatic force of Q1 on Q2 is 2.0e-5 N. • At what distance of separation between Q1 and Q2 would the force be 1.0e-5N? a) 0.02 m d) 0.007m b) 0.014 m e) 0.005 m Walker, Chapter 19 c) 0.01 m 44