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Physics B AP Review: Electricity and Magnetism Charge (Q or q, unit: Coulomb) Comes in + and – The proton has a charge of e. The electron has a charge of –e. e = 1.602 10-19 Coulombs. Name:________________ Note: The electric field inside a conductor is always zero, whether or not the conductor is charged or near some external charges. 2. Draw field around a + charge Charge distribution Positively charged objects have too few electrons; negatively charged objects have too many. If the charged object is an insulator, the excess charge is usually distributed evenly throughout; if it is a conductor, the excess charge will accumulate on the surface. + 3. Draw field around a - charge Charge is conserved In any nuclear reaction (or any process whatsoever) total charge remains constant. - Charges apply force to each other Like charges repel each other; unlike charges attract each other Coulomb’s Law kq q qq 1 F 12 2 or F 1 2 2 where k r 4 o r 4 o Applies only to spherically symmetric charges 4. Draw field around dipole - 1. Coulomb’s Law (A-177 54) Two isolated charges, + q and - 2q, are 2 centimeters apart. If F is the magnitude of the force acting on charge -2q, what are the magnitude and direction of the force acting on charge + q ? Magnitude Direction (A) 1/2 F Toward charge —2q (B) 1/2 F Away from charge -2q (C) F Toward charge -2q (D) F Away from charge -2q (E) 2F Toward charge -2q Show your work 5. + Draw field between capacitor plates +++++++++++++++++++++++++ ----------------------++ ++ Magnitude of the electric field kq q 1 E +2 +or E where k r 4 o r 2 4 o Applies only to spherically symmetric charges Electric Fields (E, unit: N/C or V/m) Start on + charges and terminate on – charges. Electric field lines indicate direction force would be on a tiny + test charge put in the field. Electric field lines are not vectors. The field vectors are tangent to the field lines. Electric field vector gives direction of electric force on a + charge placed in the field. 6/28/2017 Principle of Superposition The electric field at a given point in space is the vector sum of the electric fields due to all charges in the vicinity. The resulting vector gives the direction of the electric force on a positive charge placed in the field. 1 Bertrand Electric Polarization Electric fields cause polarization (redistribution of charge) on neutral objects Conductors are especially vulnerable to this effect. When placed in an electric field, the charges redistribute themselves so that the electric field inside the conductor is zero. Remember our electroscope experiments? The electroscope is a conductor. When a charged rod is brought near, the charges on the electroscope move. That makes the vanes separate, since they assume the same charge. The electric field inside the electroscope’s metal parts will be zero. 6. Field strength analysis (A177 20) A hollow metal sphere of radius R is positively charged. Of the following distances from the center of the sphere, which location will have the greatest electric field strength? (A) O (center of the sphere) (B) 3R/4 (C) 5R/4 (D) 2R (E) None of the above because the field is of constant strength Explain your reasoning 7. 9. Electrical polarization (PAB) Which of the following is true about the net electric field inside an uncharged conducting sphere in an external uniform electric field? (A) It is exactly the same as the external field. (B) It is in the same direction as the external field, but is weaker. (C) It is in a direction opposite to the field. (D) It produces a torque on the sphere about the direction of the field. (E) It is zero. Explain your reasoning by drawing a picture. Electric Field (A177 57) Charges +Q and -4Q are situated as shown above. The net electric field is zero nearest which point? (A) A (B) B (C) C (D) D (E) E Show your work: 10. Electrical field calculation from point charges (A182 68) 8. Electric Field (A187 17) The diagram above shows an isolated, positive charge Q. Point B is twice as far away from Q as point A. The ratio of the electric field strength at point A to the electric field strength at point B is (A) 8 to 1 (B) 4 to 1 (C) 2 to 1 (D) 1 to 1 (E) 1 to 2 Show your work: The figure above shows two particles, each with a charge of +Q, that are located at the opposite corners of a square of side d. What is the direction of the net electric field at point P ? A) B) C) D) Explain your reasoning: 6/28/2017 E) 2 Bertrand Calculating Force from Field F = Eq the following occurs when the two spheres are connected with a conducting wire? (A) No charge flows. (B) Negative charge flows from the larger sphere to the smaller sphere until the electric field at the surface of each sphere is the same. (C) Negative charge flows from the larger sphere to the smaller sphere until the electric potential of each sphere is the same. (D) Negative charge flows from the smaller sphere to the larger sphere until the electric field at the surface of each sphere is the same. (E) Negative charge flows from the smaller sphere to the larger sphere until the electric potential of each sphere is the same. 11. Electric Force from Field (A177 17) An electron is accelerated from rest for a time of 10-9 second by a uniform electric field that exerts a force of 8.0 x 10-15 newton on the electron. a) What is the magnitude of the electric field? (A) 8.0 x 10-24N/C (B) 9.1 x 10-22 N/C (C) 8.0 x 10-6N/C (D) 2.0 x 10-5 N/C (E) 5.0 x 104 N/C Show your work Explain your reasoning b) The speed of the electron after it has accelerated for the 10-9 second is most nearly (A) 101 m/s (B) 103 m/s (C) 105 m/s 7 9 (D) 10 m/s (E) 10 m/s Show your work Electrical Potential: spherical calculation Calculates potential a given distance from charge. kq q 1 V or V where k r 4 o r 4 o Applies only to spherically symmetric charges 13. Electric Potential (PAB) Electrical Potential (V, unit: Volt, V) The electric potential is a scalar value related to potential energy, which is also a scalar. Potential gets more positive as you approach positive charges. Mobile positive charges therefore like to move to positions of lower potential Potential gets more negative as you near negative charges. Mobile negative charges therefore like to move to positions of higher potential “Potential difference”, V, is usually more useful than “absolute potential”, V. Potential difference, V, is necessary for current to flow. A conducting sphere of radius R bears a positive charge Q. What could the graph above represent for that sphere? (A) Electric potential as a function of distance from the surface of the sphere. (B) Electric potential as a function of distance from the center of the sphere. (C) Electric field as a function of the distance from the surface of the sphere. (D) Electric field as a function of the distance from the center of the sphere. (E) Charge as a function of distance from the center of the sphere. Explain your reasoning 12. Electric Potential (A182 70) Two conducting spheres of different radii, as shown above, each have charge - Q. Which of 6/28/2017 3 Bertrand Electrical Potential: uniform field calculation Electrical Potential in a uniform electric field (that is, and electric field that is like the one you drew in the capacitor above) V = -Ed Electrical Potential Energy For absolute potential energy, U = qV For potential energy change, U = qV 16. Electric Potential and Potential Energy (S199 16) An electron volt is a measure of (A) energy (B) electric field (C) electric potential due to one electron (D) force per unit electron charge (E) electric charge Explain your choice. 14. Electric Potential, Field, and Force (A182 17) Two large parallel conducting plates P and Q are connected to a battery of emf , as shown above. A test charge is placed successively at points I, II, and III. If edge effects are negligible, the force on the charge when it is at point III is (A) of equal magnitude and in the same direction as the force on the charge when it is at point I (B) of equal magnitude and in the same direction as the force on the charge when it is at point II (C) equal in magnitude to the force on the charge when it is at point I, but in the opposite direction (D) much greater in magnitude than the force on the charge when it is at point II, but in the same direction (E) much less in magnitude than the force on the charge when it is at point II, but in the same direction 17. Electric Potential and Potential Energy (A187 18) Explain your reasoning The figure above shows two particles, each with a charge of +Q, that are located at the opposite corners of a square of side d. What is the potential energy of a particle of charge +q that is held at point P? A) zero B) 2 qQ/(4od) C) qQ/(4od) 15. Parallel Plate E and V (PAB) Two parallel conducting plates are connected to a constant voltage source. The magnitude of the electric field between the plates is 100 N/C. If the voltage is doubled and the distance between the plates is reduced to 1/4 the original distance, the magnitude of the new electric field is (A) 40 N/C (B) 80 N/C (C) 100 N/C (D) 400 N/C (E) 800N/C Show your work: 6/28/2017 D) 2 qQ/(4od) E) 22 qQ/(4od) Show your work 4 Bertrand 18. Charged conductor (S199 59) A positive charge Of 10-6 coulomb is placed on an insulated solid conducting sphere. Which of the following is true? 19. Equivalent Capacitances (A182 15) (A) The charge resides uniformly throughout the sphere. (B) The electric field inside the sphere is constant in magnitude, but not zero. (C) The electric field in the region surrounding the sphere increases with increasing distance from the sphere. (D) An insulated metal object acquires a net positive charge when brought near to, but not in contact with, the sphere. (E) When a second conducting sphere is connected by a conducting wire to the first sphere, charge is transferred until the electric potentials of the two spheres are equal. a) The equivalent capacitance for this network is most nearly (A) 10/7 uF (B) 3/2 uF (C) 7/3 uF (D) 7 uF (E) 14 uF Show your work: b) The charge stored in the 5-microfarad capacitor is most nearly (A) 360 uC (B) 500 uC (C) 710 uC (D) 1,100 uC (E) 1,800 uC Show your work: Explain your reasoning: Energy in a Capacitor UE = ½ C (V)2 UE: electrical potential energy (J) C: capacitance in (F) V: potential difference between plates (V) << ADVANCED TOPIC >> Capacitor Consists of two “plates” (or conductors) in close proximity. When the capacitor is “charged”, there is a voltage across the plates, and they bear equal and opposite charges. 20. Energy in a Capacitor (A187 70) A 4 F capacitor is charged to a potential difference of 100 V. The electrical energy stored in the capacitor is Capacitance (C, unit: Farad) The ability of a capacitor to hold charge. C = q / V C: capacitance (F) q: charge (on positive plate) (C) V: potential difference between plates (V) x 10-10 J -4 (D) 2 x 10 J (A) 2 x 10-8 J -2 (E) 2 x 10 J (B) 2 (C) 2 x 10-6 J Show your work: Drawing Capacitors in Circuits Capacitance of parallel plate capacitor Capacitance is related linearly with plate area, and inversely with spacing between the plates C = e0A/d C: capacitance (F) e: dielectric constant of filling 0 : electrical permittivity (8.85 x 10-12 F/m) A: plate area (m2) d: distance between plates (m) Equivalent capacitance The capacitance that a group of capacitors together possesses. For capacitors in series: 1/Ceq = Ci) For capacitors in parallel: Ceq = Ci Equivalent capacitance equations are the opposite of equivalent resistance equations. 6/28/2017 5 Bertrand Usually internal resistance of the cell causes the “terminal voltage” to be lower than the emf. 21. Parallel Plate Capacitor (A187 64) Two parallel conducting plates, separated by a distance d, are connected to a battery of emf . Which of the following is correct if the plate separation is doubled while the battery remains connected? (A) The electric charge on the plates is doubled. (B) The electric charge on the plates is halved. (C) The potential difference between the plates is doubled. (D) The potential difference between the plates is halved. (E) The capacitance is unchanged. Explain your reasoning Conductors Conduct electricity easily; i.e., metals. Have low “resistivity”. Insulators Don’t conduct electricity easily; i.e. rubber. Have high “resistivity”. Resistivity () Depends on the identity of the material, not its shape, size, or configuration. Resistors (R, unit: ohm, ) Devices put in circuits to reduce the current: The more a resistor reduces current, the higher the resistance it provides to the circuit. 22. Parallel Plate Capacitor (1988) 14. The capacitance of a parallel-plate capacitor can be increased by increasing which of the following? (A) The distance between the plates (B) The charge on each plate (C) The area of the plates (D) The potential difference across the plates (E) None of the above Explain your reasoning Calculating resistance (R) from resistivity () R = L/A 23. Calculating Resistance (PAB) Wire from the same spool is used to make two wire loops. One loop has a radius b and the other has a radius 2b. The total resistance of the smaller loop is R. What is the resistance of the larger loop? (A) R/4 (B) R/2 (C) R (D) 2R (E) 4R Show your work or explain your reasoning Current (I, unit: Ampere, A) Flow of positive charge I = Q/t Direct Current (DC) Uniform current flowing in one direction. 24. Calculating Resistance (A177 40) The five resistors shown below have the lengths and cross-sectional areas indicated and are made of material with the same resistivity. Which resistor has the least resistance? Cell What produces the current in a circuit: Battery Multiple cells in series. Below, for 2 cells: Electromotive force ( The potential, or voltage, that can theoretically be produced by the cell based on its chemistry. 6/28/2017 6 Bertrand Explain your reasoning Show your work Ohm’s Law V = IR 26. Power and Energy (A177 19) An immersion heater of resistance R converts electrical energy into thermal energy that is transferred to the liquid in which the heater is immersed. If the current in the heater is I, the thermal energy transferred to the liquid in time t is (A) IRt (B) I2Rt (C) IR2t 2 (D) IRt (E) IR/t Show your work Ohmmeter Placed across resistor or other circuit element to measure resistance when no current is flowing. Voltmeter Placed across resistor or other circuit element to measure potential change when current is flowing. V 27. Power and Energy (A187 20) A certain coffeepot draws 4.0 A of current when it is operated on 120 V household lines. If electrical energy costs 10 cents per kilowatt-hour, how much does it cost to operate the coffeepot for 2 hours? (A) 2.4 cents (B) 4.8 cents (C) 8.0 cents (D) 9.6 cents (E) 16 cents Show your work Ammeter Placed in a circuit in place of a wire to measure the current flowing in that part of the circuit. A Power in Electrical Circuits (P, unit: Watt, W) P = I V Resistors in series Energy in Electrical Circuits (unit: Joule, J) E = (P)(t) Note: the kilowatt hour is a unit of energy, not a unit of power. Req = Ri Resistors in parallel 25. Power and Energy (A182 51) The product 2 amperes x 2 volts x 2 seconds is equal to (A) 8 coulombs (C) 8 joules (E) 8 newton-amperes 6/28/2017 1/Req = Ri) (B) 8 newtons (D) 8 calories 7 Bertrand 28. Equivalent Resistance (S195 18) Show your work or state your reasoning 30. General Circuit Problems (A182 20) Parts a-c relate to the following circuit diagram, which shows a battery with an internal resistance of 4.0 ohms connected to a 16-ohm and a 20-ohm resistor in series. The current in the 20-ohm resistor is 0.3 amperes. Which two arrangements of resistors shown above have the same resistance between the terminals? (A) I and II (B) I and IV (C) II and III (D) II and IV (E) III and IV Show your work a) What is the emf of the battery? (A) 1.2 V (B) 6.0 V (D) 12.0 V (E) 13.2 V Show your work (C) 10.8 V 29. Equivalent Resistance (A177 15) A C B b) What is the potential difference across the terminals X and Y of the battery? (A) 1.2 V (B) 6.0 V (C) 10.8 V (D) 12.0 V (E) 13.2 V Show your work a) The total equivalent resistance between points X and Y in the circuit shown above is (A) 3 (B) 4 (C) 5 (D) 6 (E) 7 Show your work c) What power is dissipated by the 4-ohm internal resistance of the battery? A) 0.36 W (B) 1.2 W (C) 3.2 W (D) 3.6 W (E) 4.8 W Show your work b) When there is a steady current in the circuit, the amount of charge passing a point per unit of time is (A) the same everywhere in the circuit (B) greater at point X than at point Y (C) greater in resistor A than in resistor B (D) greater in resistor B than in resistor C (E) greater in resistor B than in resistor A 6/28/2017 8 Bertrand 33. Kirchoff’s Rules (A182 14) Kirchhoff's loop rule for circuit analysis is an expression of which of the following? (A) Conservation of charge (B) Conservation of energy (C) Ampere's law (D) Faraday's law (E) Ohm's law Explain your reasoning 31. Circuit Problem (A182 50) In the diagrams above, resistors R1. and R2 are shown in two different connections to the same source of emf that has no internal resistance. How does the power dissipated by the resistors in these two cases compare? (A) It is greater for the series connection. (B) It is greater for the parallel connection. (C) It is the same for both connections. (D) It is different for each connection, but one must know the values of . R1 and R2 to know which is greater. (E) It is different for each connection, but one must know the value of to know which is greater. Explain your reasoning Magnetic Dipole Magnetic field lines are complete loops that exit the magnet at the north pole and re-enter at the south pole. Magnetic Field (B-field) Units Tesla (SI) Gauss (1 T = 104 gauss) Magnetic Monopoles Do not exist! 32. Ohm’s Law (A177 68) Magnetic Force on Charged Particle F = qvBsin direction: Right Hand Rule 34. Magnetic Force (A187 22) In the circuit shown above, the value of r for which the current I is 0.5 ampere is (A) 0 (B) 1 (c) 5 (D) 10 (E) 20 Show your work An electron is in a uniform magnetic field B that is directed out of the plane of the page, as shown above. When the electron is moving in the plane of the page in the direction indicated by the arrow, the force on the electron is directed (A) toward the right (B) out of the page (C) into the page (D) toward the top of the page (E) toward the bottom of the page State your reasoning Kirchoff’s 1st Rule (Junction rule) The sum of the currents entering a junction equals the sum of the currents leaving the junction. Conservation of charge. Kirchoff’s 2nd Rule (Loop rule) The net change in electrical potential in going around one complete loop in a circuit is equal to zero. Conservation of energy. 6/28/2017 9 Bertrand Magnetic Fields are formed by moving charges. may exert a force on moving charges, provided a portion of the velocity is perpendicular to the field. B directed into paper E directed down Velocity of charged particle directed right q Magnetic Forces can... accelerate charged particles by changing their direction, causing charged particles to move in circular or helical paths Magnetic Force on Current-carrying Wire F = I L B sin Magnetic Forces cannot... change the speed or kinetic energy of charged particles, or do work on charged particles 36. Magnetic Force (A177 47) The magnetic force is centripetal qvBsin = mv2/r qB = mv/r A wire in the plane of the page carries a current I directed toward the top of the page, as shown above. If the wire is located in a uniform magnetic field B directed out of the page, the force on the wire resulting from the magnetic field is (A) directed into the page (B) directed out of the page (C) directed to the right (D) directed to the left (E) zero State your reasoning 35. Magnetic Force as a Centripetal Force (PAB) A magnetic field of Bo forces a proton to move in a circle of radius R. The plane of the circle is perpendicular to the magnetic field. a) Of the following, which best represents the amount of the work done by the magnetic field on the proton during one complete orbit of the circle? (A) 0 J (B) BoR (C) Bo/R (D) qvBR (E) Must know the speed of the particle. Show your work or explain your reasoning 37. Magnetic Force (S195 63) Two long, parallel wires, fixed in space, carry currents I1 and 12. The force of attraction has magnitude F. What currents will give an attractive force of magnitude 4F? 1 1 (A) 2 I 1 and I 2 (B) I 1 and I 2 4 2 1 1 (C) I 1 and I 2 (D) 2 I 1 and 2 I 2 2 2 4 I and 4 I 2 (E) 1 Show your work b) Of the following, which is the best estimate of the speed of the proton as it moves in the circle? (A) c (B) BR/m (C) eBR/m (D) eBR2/m (E) None of the above. Show your work Velocity filter Electric and magnetic fields can be used together to precisely select the velocity of a charged particle. 6/28/2017 10 Bertrand Magnetic Field for Long Straight Wire B = oI/(2r) 39. Magnetic Flux (A187 19) 38. Magnetic Field (A182 19) A rectangular wire loop is at rest in a uniform magnetic field B of magnitude 2 T that is directed out of the page. The loop measures 5 cm by 8 cm, and the plane of the loop is perpendicular to the field, as shown above. The total magnetic flux through the loop is (A) zero (B) 2 x 10-3 Tm -3 (C) 8 x 10 Tm (D) 2 x 10-1 Tm -1 (E) 8 x 10 Tm Show your work Two long, parallel wires are separated by a distance d as shown above. One wire carries a steady current I into the plane of the page while the other wire carries a steady current I out of the page. At what points in the plane of the page and outside the wires, besides points at infinity, is the magnetic field due to the currents zero? (A) Only at point P (B) At all points on the line SS' (C) At all points on the line connecting the two wires (D) At all points on a circle of radius 2d centered on point P (E) At no points Explain your reasoning Induced Current A system will respond to oppose changes in magnetic flux. Changing the magnetic flux can generate electrical current. Faraday’s Law of Induction = -NB/t Hand Rule for magnetic force on moving positive charge Place fingers in direction of velocity. Then rotate your wrist so that your fingers can bend into the direction of the field. Your thumb gives direction of the force. Hand Rule for magnetic force on moving negative charge Use the method described above, then flip your thumb 180o. Alternately, you may use your left hand. To generate voltage = -B/t = -(BAcos)/t Change B, Change A, or Change Hand Rule for magnetic force on current in wire Place fingers in direction of current. Then rotate your wrist so that your fingers can bend into the direction of the field. Your thumb will be pointing in the direction of the force. 40. Faraday’s Law (A187 66) Hand Rule for fields where current is straight Curve your fingers. Place thumb in direction of current. Your curved fingers point in direction of curved magnetic field. Hand Rule for fields where current is circular Curve your fingers. Place curved fingers in direction of current. Your thumb points in direction of magnetic field in center of circular current. Magnetic Flux (B, unit Webber, Wb) The product of magnetic field and area. B = BAcos B: magnetic flux in Webers (Tesla meters2) B: magnetic field in Tesla A: area in meters2. : angle between area and magnetic field. 6/28/2017 A uniform magnetic field B that is perpendicular to the plane of the page passes through two loops, as shown above. The field is confined to a region of radius a, where a < b, and is changing at a constant rate. The induced emf in the wire loop of radius b is . What is the induced emf in the wire loop of radius 2b ? 11 Bertrand (A) Zero 2 (E) 4 (B) (C) Explain your reasoning (D) 2 Show your work or explain your reasoning 41. Faraday’s Law (A182 67) A square loop of wire of resistance R and side a is oriented with its plane perpendicular to a magnetic field B. as shown above. What must be the rate of change of the magnetic field in order to produce a current I in the loop? (A) IR/a2 (B) la2/R (C) la /R (D) Ra/l (E) IRa Show your work Lenz’s Law Induced current will flow in a direction so as to oppose the change in flux. 43. Lenz’s Law (PAB) A single circular loop of wire in the plane of the page is perpendicular to a uniform magnetic field B directed out of the page, as shown above. If the magnitude of the magnetic field is increasing, then the induced current in the wire is (A) directed upward out of the paper (B) directed downward into the paper (C) clockwise around the loop (D) counterclockwise around the loop (E) zero (no current is induced) Explain your reasoning Motional emf Faraday’s law can be used to show that a wire moving in a magnetic field generates a potential equivalent to = BLv 42. Motional emf (A182 41) A wire of constant length is moving in a constant magnetic field, as shown above. The wire and the velocity vector are perpendicular to each other and are both perpendicular to the field. Which of the following graphs best represents the potential difference between the ends of the wire as a function of the speed v of the wire? 6/28/2017 12 Bertrand