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Understanding Electrostatics: Electric Charge and Coulomb's Law

Learn about electric charge characteristics of materials, Coulomb's Law, electric field basics, and exercises on electric force and fields in this homework assignment. Discover how charges interact and the effects of electric fields.

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Understanding Electrostatics: Electric Charge and Coulomb's Law

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  1. Electrostatic Electricity, Electric Charge (CH 15) (with answers) Homework No. 1 (Electrostatics) Due date: October 4 or 5 October 2016 Name: _____________________ • If you rub a glass rod with a silk cloth: a) what charge polarity will the glass rod acquire? A: Glass is positive); b) What method of charge transfer is being used? A: • If you charge a glass rod and balloon each with a silk cloth, will the rod and balloon attract or repel each other? A: • No. 23 In calculating planetary orbits around the sun, why can astronomers safely ignore the electric force? A:. • No. 26 Coulomb’s Law is also called an inverse square law. What does it tell you about the relationship between force and distance? A.: • An electron and a proton are separated by 2.0 nm. Using the Coulomb’s Law we can calculate the magnitude of the force on the electron, F = k(q1 x q2)/r2.= 5.8x 10-11 N; What is the net force on the system? A: • 6) The electric field due to negative charge (a) varies as 1/r; (b) points toward the charge, (c ) points away from the charge or (d) has a finite charge. A: • Could the electric field due to two charges ever be zero at some location nearby? If yes, describe and sketch the situation. A: q2

  2. Electric Charge Characteristics of Materials Scientists have ranked materials in order of their ability to hold or give up electrons. This ranking is called the Triboelectric series. TRIBOELECTRIC SERIES your hand glass nylon wool fur MORE POSITIVE silk paper cotton hard rubber polyester polyvinylchloride plastic If these materials are rubbed together, the one higher on the list gives up electrons. Thus becomes positively charged.

  3. Electric Charge and Electric Field The electric charge q, is a fundamental property of matter. It is associated with particles that make up the atom: electron and proton. Electron charge -e = -1.60 x 10-19 C. Proton +e = 1.60 x 10-19 C. Neutron has 0 C. The SI unit of an electric charge is the Coulomb C; [C = As}. It is equal to the charge of approximately 6.241×1018electrons. Proton’s mass is 104 times larger than the mass of an electron. Because the (net) electric charge on an object is caused by a deficiency or an excess of electrons it is an integer with a symbol q and a plus or minus sign that indicates whether the object has a deficiency (+q) or an excess (–q) of electrons. q = ± ne[C or As] An electric field E, is a space radiated by electric charges q, and acted upon by an electric force F. Electric field direction is the direction experienced by the positive charge. E = F/q [V/m] F = Eq [(V/m) As = Ws/m = N]; (Note: Nm = Ws)

  4. Coulomb’s Law and Electric Force Following Benjamin Franklin’s work, electrical research advanced by leaps. Quantitative measurements were carried out in 1785 by the French physicist Charles-Augustin de Coulomb (1786----1806). He showed that attraction (or repulsion) between given (electric) charges, q varied inversely as the square of their distance, r from each other. It became known as the Coulomb’s Law where Electric force, F between two electric charges between two points is: F = k(q1 x q2)/r2 ; k = 9.00 x109 Nm2/C2 F = [(Nm2/C2)x C2/m2] = [N] W= Fxm [Nm] Example: Two point charges q1 = -1 nC and q2 = +2 nC; distance, r between them is 0.30 m. What is the electric force, F on each particle? A: F = 9.00 x 109 Nm2/C2 x (1x10-9 C x 2x10-9 C)/0.09 m2 = 18.0 x 10-9 N/0.09 F12 0.30m F21 = 18.0 x 10-9 N/9x 10-2 = 0.20 x 10-6 N; F = 0.20 μN

  5. Coulomb’s Law and Electric Force Exercises Exercise 21, Ch. 15 Compared to electric force the gravitational force between two protons is a, about the same, b, somewhat larger, c, very much larger, d, very much smaller. A.: 21 d

  6. What is an electric field? • The electric force, like the gravitational force, is an “action at a distance” force. Its range is infinite. The electric field is a domain where the presence of electric charges exert an electric force. Charges in one field can interact with charges in another one. The electric field is a vector field that enables us to determine the force exerted on a charge in a particular location. • An electric field E [V/m],is the region of space surrounding electrically charged particles, q[As] where electric charges are acted upon by an electric force F. E = Fq/qo • E = k(qox q)/qor2 ; k = 9.00 x109 [Nm2/C2] • E = kq/r2 [Nm2/C2/m2] = [N/C] • Exercise: • The electric field due to positive charge (a) varies as 1/r; (b) points toward the charge, (c ) points away from the charge or (d) has a finite charge. Hint: See the sketch of Ligth Point Charges. 41c

  7. Electrostatic Electricity, Electric Charge (CH 15) (with answers) Homework No. 1 (Electrostatics) Due date: October 4 or 5 October 2016 Name: _____________________ • If you rub a glass rod with a silk cloth: a) what charge polarity will the glass rod acquire? A: Glass is positive); b) What method of charge transfer is being used? A: By contact • If you charge a glass rod and balloon each with a silk cloth, will the rod and balloon attract or repel each other? A: attract • No. 23 In calculating planetary orbits around the sun, why can astronomers safely ignore the electric force? A: 23c Objects are electrically neutral. • No. 26 Coulomb’s Law is also called an inverse square law. What does it tell you about the relationship between force and distance? A.: Force depends on inverse square of the distance between the charges. • An electron and a proton are separated by 2.0 nm. Using the Coulomb’s Law we can calculate the magnitude of the force on the electron, F = k(q1 x q2)/r2.= 5.8x 10-11 N; What is the net force on the system? A: • 6) The electric field due to negative charge (a) varies as 1/r; (b) points toward the charge, (c ) points away from the charge or (d) has a finite charge. A: • Could the electric field due to two charges ever be zero at some location nearby? If yes, describe and sketch the situation. A: q2 F2 F1

  8. Electric Potential, Voltage and Battery (CH 16/17) EXPERIMENT NO. 2 • Electric Potential Energy • Electric Potential Difference, Voltage • Equipotential Surfaces • Electric Potential Energy between Charges • What have we learned? • What is a Battery? • How does a battery produce electric current? • Organic Cell used in the Experiment • Electrode Potentials • Organic Cell Experiment • Quiz No. 2 • Homework No. 2 • New Terminology • SI-International System of Units

  9. Glen Canyon Dam and Hydroelectric Power Plant 1956 Glen Canyon Dam produces electrical power through the use of the gravitational force of falling or flowing water. It is 710 ft. high and 300 ft. wide at its base. It has an installed capacity of 1,296 MW.

  10. Electric Potential Difference The electric potential difference ΔV between any two points in space (commonly called Voltage) is the work done per unit positive charge between those two points, or the change in electric potential energy per unit positive charge. In equation form, this relationship is ΔV = ΔU/q or ΔV = Work/q [J/C or V] ΔV = (Eqd)/q = Ed Potential difference is commonly called voltage, and the symbol is just V. The potential difference depends on characteristics of charged plates that is, the electric field they produce (E) and their separation (d). The positively charged plate is at a higher electric potential than the negatively charged one by an amount ΔV or simply Voltage, V.

  11. Electric Potential Energy An electric field E, between plates A and B is a space where electric charges q, are acted upon by an electric force F. E = F/q [V/m] Suppose electric charge q is moved against electric field, E from the negative plate A to the positive plate B. An external electric force required to accomplish this is F = Eq The work done is Work = Fxd By moving the charge from plate A to plate B the external force has increased the charge’s electric potential energy, U. ΔU = UA - UB = Eqxd B d E = F/q q A

  12. Electric Potential Surfaces Equipotential surfaces also called equipotential are surfaces on which a charge has the same potential energy. They are perpendicular to the electric field on which it takes no work to move charges from one point to another. ΔV = Work/q [J/C or V] ΔV = Ed

  13. Example 16.1 Moving a Proton, Parallel Plates and Potential Difference • Plates are 1.5 cm apart. Electric field is uniform with a magnitude is 1500 NC. • What is the change in the proton’s electric potential energy? • What is the electric potential difference (voltage) between the plates? • Discussion: • The change in potential energy can be computed from the work done to move the charge. • b) The potential difference between the two plates can be determined by dividing the work done by the charge moved.

  14. Electric Potential Difference Due to a Point Charge The potential difference between two points in an electric field is determined by the same equation ΔV = ΔU/q or ΔV = Work/q. Because the electric field strength varies, the math is complicated because the work is done by a varying force. Therefore, the potential difference between two points at distances rA and rBis ΔV = kq/rA- kq/rB[k = 9.00x109 Nm2/C2] • Electric potential increases as we consider locations nearer the positive charges or further away from negative charges. • Electric potential decreases as we consider locations further from positive charges or nearer to negative charges.ΔV = kq/r

  15. What have we learned? Electricity is the set of physical phenomena associated with the presence or flow of an electric charge. Electric current is a flow of electrically charged particles. I = q/t, [A] Electric charge, q is the fundamental physical property of matter like atoms that causes it to experience a force when close to other electrically charged matter, positive or negative. All atoms are made up of still tinier particles: neutrons, protons (+) and electrons (-) Electric field is an electric charge produced without movement. (See above the electric field surrounding a positive and negative charge.) E = F/q [V/m] Electric potential or Voltage is the capacity of an electric field to do work on an electric charge, to move it between two specified points. The difference between two electric potentials is Voltage, [Volt or V] The reference point is the Earth or Ground. ΔV = ΔU/q or ΔV = Work/q [J/C or V] 15

  16. What is a Battery? Battery cell converts stored chemical energy into useful potential electrical energy. Once an external connection is made between its positive and negative terminals a chemical reaction is initiated that generates electrons at electrode to supply the current to the external circuit. Four cells are in parallel. A battery is a device that stores electrical energy. Four cells are in series. 16

  17. How does a battery produce electric current? • An electrolyte and two unlike metal electrodes cause ions of both metals to dissolve. • One electrode (cathode) becomes more negatively charged than the other (anode). • The other electrode (anode) is at a higher potential than the cathode. It receives negatively charged electrons. (Electrons move to regions of higher potential.) There is a potential difference across the terminals. The anode is designated the positive terminal and the cathode the negative. • This potential difference (V, Voltage) between the two electrodes causes a current or a flow of electric charges (electrons), in the wire. Simultaneously in the cell, the positive ions flow from the cathode to the anode. • I = q/t; [A = C/s]; q = nxe; e =1.6x 10-19 [C or As] Inserted into a circuit, a battery is capable of giving energy to the electrons in the wire (at the expense of its own energy), which in turn delivers that energy to circuit elements external to battery.

  18. Organic Cell’s Essential Electric Components • Anode is at a higher potential than the cathode. It receives negatively charged electrons. (Electrons move to regions of higher potential.) The direction of electric current is, by convention, opposite to the direction of electron flow-thus electrons are considered to flow toward the anode electrode while current flows away from it.) • Cathode is the negative electrode. It is an electrode through which electric current flows out of a polarized electrical device. • Electrolyte is the medium that provides the ion transport mechanism between the cathode and anode. • A Cation is a positively charged ion, i.e., one that would be attracted to the cathode in electrolysis. It has fewer electrons than protons. The opposite is Anion. Electrolysis is a chemical process that produces electricity. AWIM 18

  19. About the Organic Cell used in the Experiment? • An organic cell is an item that contains an electrolyte and two electrodes producing electricity by chemical reaction. • In our experiment we’ll use lemon and potato as organic electrolytes (other fruit are also effective like banana and cucumber that are derived from a living organism). Lemons juice is an electrolyte called citric acid. Potato has an electrolyte made of Sodium (Na), Potassium (K) and Chloride (Cl) ions (phosphoric acid). • Copper and Zinc are two metals that serve in our experiment as electrodes that attract positive (Co) and negative (Zn) ions during a chemical reaction in the electrolyte. Copper electrode is positive at +0.34 V that attracts negative (Zn) or (Ni) ions during the chemical reaction. • Zinc and Nickel electrodes have free electrons with a potential voltage of -0.76 V and -0.25 V. • (Magnesium (Mg), Lead (Pb), Nickel (Ni) and Cadmium (Cd) are used commercially.)

  20. Standard Electrode Potentials in Aqueous Solution at 25°C. (aq)=aqueous or water solution; (s)=solid phase; (l)=liquid phase Aluminum (Al), Zinc (Zn), Nickel (Ni), and Copper (Cu) will be used in experiment Table of Standard Electrode Potentials taken from hyperphysics.phy-astr.gsu.edu/hbase/tables/2010/19/13 Electrode Potential determines the output voltage of an electro-chemical cell.

  21. Electrode Potential determines the output voltage of an electro-chemical cell • Each chemical element is characterized by its excess (-) or lack of (+) free electrons. • Electrodes have a potential to release FREE electrons (-) to those that don’t have any FREE electrons (+) Ex 1: Zinc, Zn = -0.76 V Ex 2: Nickel, Ni = -0.23 V Ex 3: Copper, Cu = +0.34 V • Voltage difference between Cu and Zn electrodes in a lemon electrolyte can be calculated ahead of an experiment. Voltage difference between Cu to Zn electrodes = +0.34V – (-0.76V) = 1.10V (Test 1) Voltage difference between Cu to Ni electrodes = +0.34V – (-0.23V) = 0.57V (Test 4) (Important note: An anode is an electrode through which electric current flows out of (and electrons into) a polarized electrical device. The direction of electric current is, by convention, opposite to the direction of electron flow. Therefore the electrons flow out (and current into) the cathode electrode Zn and into (and current out of) anode electrode Cu.) AWIM 21

  22. What is Needed to Conduct this Experiment? • Electrolyte (natural fruit: lemon, potato (other fruit can be used) • Electrodes to insert into the fruit (one inch a part, half an inch deep) • 3.Voltmeter to measure voltage • A Pair of Red and Black Copper Wires (with alligator clips to connect electrodes with a voltmeter) • A Team of two Students (to make connections and write down the measurements) • Report and Discuss Results • Use the napkin to clean electrodes and save it all in the plastic bag.

  23. Organic Cell Experiment Tests Measure the voltage across Copper and Zinc electrodes placed parallel to each other in a fruit one inch apart and ½ inch deep! Connections: Use black alligator clips to connect the Copper electrode (-) with voltmeter (-); Use red alligator clips to connect the Zinc electrode (+) with voltmeter (+); Set the voltmeter in the 20 VDC range and turn it ON; Measurement: Read the voltage and make a note: _____ Volts Record measurements and observations in the Data Sheet

  24. Test No. 1 Potato CELL is an Organic CELL that can Generate Electricity VOLTMETER Set on 20 VDC scale ZINC electrode (anode) COPPER electrode Use Potato instead of Lemon in this test only!

  25. Test No. 2 Lemon CELL is an Organic CELL that generates the same Electric Potential as does the Potato Cell VOLTMETER Set on 20 VDC scale ZINC electrode (anode) COPPER electrode

  26. Test No. 3 TWO LEMON CELLS Connected in Series Produce TWO TIMES Voltage of a Single One VOLTMETER SET ON 20 VDC SCALE 1.78 volt COPPER electrode ZINC electrode

  27. Test No. 4 Using Nickel instead of Zinc Electrode the Lemon CELL generates LOWER Electric Potential VOLTMETER Set on 20 VDC scale NICKEL electrode COPPER electrode .45 V

  28. Organic Cell Experiment Test Results Name_____________________________ • Purpose: • Develop an understanding the role an electrolyte and electrodes have in a the process of generating battery’s electric potential. • Test No. 1 Estimate: 1.10 Volts; Measured: ___V; Electrode: Cu/Zn; Electrolyte: 1 Potato • Test No. 2 Estimate: 1.10 Volts; Measured: ___V; Electrode: Cu/Zn; Electrolyte: 1 lemon • Test No. 3 Estimate: 2.20 Volts; Measured: ___V; Electrode: Cu/Zn; Electrolyte: 2 Lemon • Test No. 4 Estimate: 0.57 Volts; Measured: ___V; Electrode: Cu/Ni; Electrolyte: 1 Lemon • Explain why the electric potential is the same in test No. 2 as in Test No. 1?_____________________________________________________________________ • Explain why the electric potential measured in test no. 3 is double what was measured in the test no. 2___________________________________________________________ • Explain why the electric potential measured in the test no. 4 is one half of what you have measured in the test no. 3:________________________________________________

  29. Quiz No. 2 Due Date: October 11, 12, 2016 Name:__________________________ 1. If the electric potential is constant inside and throughout an object, what is the electric field in the object? ________________________________________________________________________ 2. What basic functions do battery cells provide? (Of what use are batteries?)________________ ______________________________________________________________________________ 3. What do you need to make a simple battery? (Define the necessary components.) __________ _____________________________________________________________________________ 4. How does a battery work? (Describe how the constituent parts interact.) _________________ __________________________________________________________________________________ 5. Why do engineers sometimes choose not to use the materials that provide the best performance? ______________________________________________________________________

  30. Homework No. 2 Due Date: October 11, 12, 2016 Name:_________________________ • The Si unit of electric potential is: a) joule, b) newton, c) newton-meter, d) joule per coulomb? • If two locations are at the same potential, does it take net work to move a charge from one location to another? Y or N • Equipotential surfaces are those surfaces in which a) the potential is constant, b) the electric field is zero, c) the potential is zero. • Potential difference is commonly called voltage. T or F • The potential difference between two parallel plates is the product of the electric field between the plates and the square of the distance separating the plates. T or F • The digital multimeter can be used to measure a) voltage, b) current, c) resistance, d) all of these. • A neutral atom that takes on or loses an electron is called a(n) a) anode, b) cathode, c) ion, d) nerd. • In the organic battery cell experiment, Cu and Zn produced an estimated standard electrode potential difference of 1.10 volts. What voltage would you expect if you substitute Al for Zn? ________ volts • Presuming you could invent a new battery, what electrode materials would you try to use to maximize the output voltage? _____________________ and ____________________. • In an organic battery cell, the fruit used to provide the electrolyte has a great influence on the voltage the battery can generate. T or F • What is the voltage across six 1.5 volt D cells when they are connected in (a) series, and (b) parallel? (a)___________ volts, (b)____________ volts • You have two pairs of 1.5 volt D cells (4 batteries). The batteries in each pair are connected in series and the two pairs are connected in parallel. What is the total voltage of this arrangement? ________ volts • You have two pairs of 1.5 volt D cells (4 batteries). The batteries in each pair are connected in parallel and the two pairs are connected in series. What is the total voltage of this arrangement? ________ volts 14. The negative battery terminal is called the _________ and the positive terminal is called the ___________.

  31. New Terminology • SI Units:--------------a system of physical units based on the meter, kilogram, second, ampere, kelvin • Hydroelectricity--- production of electrical power through the use of the gravitational force of falling or flowing water. • Electric potential-- the capacity of an electric field to do work on an electric charge, to move it between two specified points. The difference between two electric potentials is Voltage, [Volt or V] The reference point is the Earth or Ground. • Electric current-----a flow of electrically charged particles. I = q/t, [A] • Electric field---------an electric charge produced without movement. (See above the electric field surrounding a positive and negative charge q. An electric field E, is a space radiated by electric charges q, and acted upon by an electric force F where E = F/q = kq/r2. • Electric Force-------- • Power----------------- the rate at which electric energy is transferred by an electric circuit. The unit of electric power is one Watt (W = VxA). • Electrical Energy--- a physical quantity that expresses over time the rate at which electric power W is being transmitted Whr. • Battery---------------- converts stored chemical energy into useful electrical energy. Once an external connection is made between its positive and negative terminals a chemical reaction is initiated that generates electrons at the anode to supply the current of the battery to the external circuit. Not all batteries can be recharged. • Electrodes------------ are the two parts of a battery where the battery‘s chemical reactions take place. The electrodes extend to the outside of the battery, where they connect to its external circuit. • Cathode--------------- is the negative electrode where the electrons are released out of (and current into) the external circuit. • Anode------------------ the positive electrode that acquires electrons into (and current out of) the external circuit. • Electrolyte------------ the medium that provides the ion transport mechanism between the cathode and anode. • Ion---------------------- an atom or molecule in which a total number of electrons is not equal to the total number of protons, giving the atom a net positive or negative charge. • The US Patent------- A grant made by the government that confers upon the creator of an invention the sole right to make, use, and sell that invention for a set period of time.

  32. SI-International System of Units Symbol Name Unit SI Conversion J Work Joule kgm/s2 = Nm = Ws = CV I Electric current Ampere A = C/s q Electric charge Coulomb C = A E Electromotive force, Potential difference Volt J/C = W/A = Nm/C ρResistivity Resistivity Ωm P Electric power Watt W = VA = Nm/s = kg m/s3 E Electric field strength Volt per meter V/m H Magnetic field strength Ampere per meter A/m B Magnetic flux density, Induction (F/qv) Tesla T = Wb/m2 μ Permeability henry per meter Tm/A= H/m = kgm/(As) μ0 Permeability of free space 4 π x 10-7N/A2 F Force of motion N 1 N = 1 kg m/s2 v Velocity m/s Resistance Ohm V/A = 1 Ω = 1 kg·m2·s-3·A-2 in Inch Inch 0.0254 m or 25.4 mm T Tesla Tesla Vs/m2 = N/Am = Wb/ms2 N Newton Newton Kgm/s2 Wb Weber Weber 1 V·s = 1 T·m2 = 1 J/A; J Joule1Nm; 1kgm/s2 ; 2.78 x 10-7 kWh; 2.39 x 10-4 kcal; 9.48 x10-4 BTU P Mechanical power 1hp 550 ft.-lb/s = 1 W Kg Kilogram mass 1.0 kg x 9.8m/s2 1N Ω

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