Electrostatics 169
Electrostatics Electrostatics the study of electrical charges that can be collected and held in one place. Types of Charge Also referred to as Static Electricity Benjamin Franklin noticed that two different charges existed; he called them positive and negative A Microscopic View of Charge How do objects become charged? Objects become charged by gaining or loosing electrons. Neutral Atom Positive Ion Negative Ion contains all electrons loses 1 or more electrons gains 1 or more electrons Separation of Charge by Friction Rubber and Fur 1890, J.J. Thompson discovered that all materials contain light, negatively charge particles he called electrons. Glass and Silk Positive (Fur), Negative (Rubber) Electrons from wool are transferred to rubber Positive (Glass), Negative (Silk) 170
Conservation of Electric Charge 1. The total charge in any closed system never changes. (The combined total charge of two objects remains the same.) 2. Individual charges can neither be created nor destroyed; they can only be transferred from one object to another. Types of Materials Insulators materials through which charges will not move easily. Ex glass, dry wood, most plastics, cloth, distilled water & dry air. DEMONSTRATION Tesla Coil, Aluminum Sheet, Rubber Pad, Flourescent light bulb. Use tesla coil to demonstrate the ability for difference materials to conduct charge. Conductors materials that allow charges to move about easily. Ex metals, water solution Can air become a conductor? DEMO: Faraday Cage Normally, the air surrounding a cloud would be a good enough insulator to prevent a discharge of electrons to Earth. Yet, the strong electric fields surrounding a cloud are capable of ionizing the surrounding air and making it more conductive. The ionization involves the shredding of electrons from the outer shells of gas molecules. The gas molecules which compose air are thus turned into a soup of positive ions and free electrons. The insulating air is transformed into a conductive plasma. The ability of a storm cloud's electric fields to transform air into a conductor makes charge transfer (in the form of a lightning bolt) from the cloud to the ground (or even to other clouds) possible. Semiconductors - A material that conducts charge better than an insulator but worse than a conductor. Ex silicon, germanium, humans Superconductors a material that conducts charge with zero resistance below a certain (critical) temperature. Ex ceramic oxide, aluminum, tin, lead, and zinc Grounding Removing excess charge from a charged body by connecting it to the Earth. Leakage The discharging of a charged object due to the acceptance of electrons by the air. 171
Robert Millikan s Oil Drop Experiment In 1909, Robert Milikan performed an experiment at the University of Chicago in which he observed the motion of tiny oil droplets between two parallel metal plates. The oil droplets were charged by friction in an atomizer and allowed to pass through a hole in the top plate. Initially the droplets fell due to their weight. The top plate was given a positive charge as the droplets fell, and the droplets with a negative charge were attracted back upward toward the positively charged plate. By turning the charge on and off, Millikan was able to watch a single oil droplet for many hours as it alternately rose and fell. Explain why electric charge is quantized. Electric charge is quantized because all electrons have one specific charge. Therefore, charge can only occur in discrete amounts of charge ± e, or ± 2 e, or ± 3 e, and so on. Elementary Unit of Charge the amount of negative charge that the electron (- e) has and positive charge that a proton has (+e). e = 1.60 x 10-19 C 1. How many elementary charges are in one coulomb of charge? æ 1 e ö è1.60 x 10 C ø 18 1C ç = 6.25 x 10 elementary charges -19 2. An object has acquired a charge of 3.2 x 10-17 C. How many excess electrons are on the object? -17 1 electrons 2-3.2 x 10 C æ ö ç = 200 electrons (2.0 x 10 e) -19 è- 1.60 x 10 C ø 3. A glass rod loses 2500 electrons after being rubbed with silk. What is the charge on the rod? The silk? -19 æ- 1.60 x 10 C ö -16 2500 electrons = 4.0 x 10 C ç 1 electrons è ø 172
4. A balloon gains a charge of 6.4 µc after being rubbed on your hair. How many excess electrons is this? -6 1 electrons -13-6.4 x 10 C æ ö ç = 4.0 x 10 C -19 è- 1.60 x 10 C ø 5. A helium nucleus is known as an alpha particle. It consists of two protons and two neutrons. What is the charge on an alpha particle? -19 æ+ 1.60 x 10 C ö -19 2 protons = 3.2 x 10 C ç 1 proton è ø 6. Which of the following charges are possible for an object to have? (A) -3.2 x 10-19 C (B) 4.8 x 10-19 C (C) 5.6 x 10-19 C (D) 1.6 x 10-20 C (E) 5.6 C 2 e 3 e 3.5 x 10 19 e 7. The top quark was one of the last quarks to be discovered by particle physicists in particle accelerator experiments. It has a fractional electric charge of +2/3 e. What is this charge in coulombs? -19 2 æ+ 1.60 x 10 Cö -19 + e = 1.07 x 10 C 3 ç 1 e 1.1 x 10-19 C è ø Charging by Conduction Conduction charging a neutral object by touching it with a charged object. Initial State Transfer of Charge Final State 0 0 Total Charge = 0 Flow of electrons Total Charge = 0 e Initial State Transfer of Charge Final State - 20-20 Total Charge = - 40 Flow of electrons Total Charge = - 40 173
Initial State Transfer of Charge Final State 20 20 Total Charge = + 40 Flow of electrons Total Charge = + 40 Initial State Transfer of Charge Final State 5 5 Total Charge = + 10 Flow of electrons Total Charge = + 10 Initial State Transfer of Charge Final State 15 e 3 3 12 e 3 Total Charge = + 9 Flow of electrons Total Charge = + 9 Three identical metal spheres are mounted on insulating stands. Initially, sphere A has a net charge of q and spheres B and C are uncharged. Sphere A is touched to sphere B and removed. Then sphere A is touched to sphere C and removed. What is the final charge on sphere A? 1/4 th of q 174
Separation of Charge on Neutral Objects Sketch the charge distribution on the soda can. Sketch the charge distribution as a negatively charged rod is brought nearby. Sketch the charge distribution as a positively charged rod is brought nearby. Negative charges in the neutral object are attracted to the positively charged object, and the positive charges in the neutral object will be repelled. The neutral object will remain neutral, but the positive and negative charges (inside neutral object) will be separated. Polarization to cause one side of an object to become negative, and the other side to be positive. Charging by Induction Induction causing a neutral object to become charged without direct contact between the charged object and the neutral object. 175
The Needle Electroscope 1. Conducting plate Use Electroscope Video In 1748 french physicist Jean Antoinne Nollet invented the first electroscope. Englishmen, Abraham Bennet invented the gold-leaf electroscope in 1786. In 1912, Victor Hess took a gold leaf in a hot air balloon up to 17,500 ft to find that as altitude increases radiation increases. 2. needle pivot 3. leaves 4. 1. What is the position of the see-saw when the electroscope is uncharged? Needle is standing vertically (up and down) 2. What is the position of the see-saw when the electroscope is charged? Needle is standing diagonally Induced Charge Separation Negative Rod Positive Rod Electron flow: Electron flow: Reaction of see-saw: Needle repels from pivot. Reaction of see-saw: Needle repels from pivot. Conclusions: Net charge on electroscope remains neutral. 176
Charging by Conduction Step 1 Step 2 Electron flow: Touch the conducting plate of the electroscope with a negatively charged rod. Reaction of see-saw: Needle is negative. Step 1 Step 2 Electron flow: Touch the conducting plate of the electroscope with a positively charged rod. Reaction of see-saw: Needle is positive. Conclusions: Net charge on electroscope is the same as the charge on the rod / strip. 177
Electron flow: Charging by Induction Step 1 Step 2 Step 3 Electron flow: Bring the negative rod close to the electroscope so there is a noticeable reaction by the seesaw. Hold the rod in place, and ground the electroscope. Reaction of see-saw: Needle is positive. Step 1 Step 2 Step 3 Bring the positive rod close to the electroscope so there is a noticeable reaction by the seesaw. Principles of Induction Hold the rod in place, and ground the electroscope. 178 Reaction of see-saw: Needle is negative. The charged object is never touched to the object being charged by induction. The charged object does not transfer electrons to or receive electrons from the object being charged. The charged object only served to polarize the object being charged. The object being charged is touched by a ground; electrons are transferred between the ground and the object being charged (either into the object or out of it). The object being charged ultimately receives a charge that is opposite that of the charged object which is used to polarize it.
Negative Positive Rod Rod Flow of electrons: Testing a Charged Electroscope Reaction of see-saw: Repels farther from pivot. Reaction of see-saw: Attracts closer to pivot. Conclusions: Electroscope is positively charged. Reaction of see-saw: Attracts closer to pivot. Reaction of see-saw: Repels farther from pivot. Conclusions: Electroscope is negatively charged. 179
= 8.99 x 10 9 N m 2 /C 2 Electric Force qq F=k e r 2 Electric Force The Electrostatic Force (Coulomb s 1 2 Law) Charge Separation What causes the charged balloons to push or pull one another? An electrostatic force causes the balloons to push or pull on one another due to their charge. Factors that effect Electrostatic Force 1. size of charge 2. distance Point Charge a charged conducting sphere interacts with other charged objects in a manner that it is as though its charge were located at its center. Coulomb s Law the magnitude of the force between two charges separated by a distance (r), can be found using. 180
Which object below experiences a greater force, A or B? A B 3.0 x 10-6 C Left 6.0 x 10-6 C q1 q2 q3 2.0 m 5.5 m Both experience the same amount of force. Right Calculate the electric force between them if their centers are 7.5 x 10-1 meters apart. -6-6 q1q 2 9 2 2 (3.0x10 C)(6.0x10 C) e 2-1 2 F =k = 8.99x10 N m / C =.29N r (7.5x10 m) If object A has its charge doubled, what is the new force it exerts on B? What is the force that B exerts on A?.58 N Coulomb s Law with Three Charges Three charges exist in a closed system. If q1 = +1.2 µc, q2 = -3.4 µc, and q3 = +6.8 µc, what is the net force on charge q2 in each situation? -6-6 q1q 2 9 2 2 (1.2x10 C)(3.4x10 C) qonq 2 2 F =k =8.99x10 Ngm /C =.0092N 1 2 r (2.0m) -6-6 q1q 2 9 2 2 (6.8x10 C)(3.4x10 C) qonq 2 2 F =k =8.99x10 Ngm /C =.0069N 3 2 r (5.5m) Fnet =.0023 N Left 181
F onq E= q at 15º N of E Electric Fields How can a force be exerted across what seems to be empty space? In trying to understand electric force, Michael Faraday developed the concept of an electric field. According to Faraday, a charge creates an electric field about it in all directions. If a second charge is placed at some point in the field, the second charge interacts with the field at that point. The resulting force is the result of a local interaction that travels along the electric field lines. Electric Field a vector quantity that relates the force exerted on a test charge to the size of the test charge. All charged objects create an electric field which extends outward into the space which surrounds it. The charge alters that space, causing any other charged object that enters the space to be affected by this field. Test Charge a small positive charge that is placed near another charge to produce a force (attractive or repulsive) in order to observe an electrical field. Why should the test charge be small? The test charge also exerts a force on q. It is important that the force exerted by the test charge doesn t move q to another location, and thus change the force on q and the electric field being measured. Calculating the Strength of an Electric Field Units - N/C (Newton / Coulomb) 1. An electric field is to be measured using a positive test charge of 3.0 x 10-6 C. This test charge experiences a force of 0.12 N acting at an angle of 15º. What is the magnitude and direction of the electric field at the location of the test charge? F 0.12N q 3.0x10 C 4 E= = =4.0x10 N/C -6 2. A charge of +1.0 10-5 C experiences a force of 0.2 N when located a certain position in the electric field produced by a second charge. What is the electric field strength at that point? F 0.2N q 1.0x10 C 4 E= = =2x10 N/C -5 182
REMEMBER ELECTRIC FIELDS EXIST IN THREE DIMENSIONS Drawing Electric Fields 1. The strength of the electric field is indicated by the spacing between lines. The field is strong where the lines are close together. It is weaker where the lines are spaced farther apart. Electric field is greatest at locations closest to the surface of the charge and least at locations further from the surface of the charge. 2. There is never a component of electric force which is directed parallel to the surface. The electric force, and thus the electric field, is always directed perpendicular to the surface of an object. 3. Field lines always leave a positive charge and enter a negative charge. 4. The direction of the arrow shows the field direction. 5. Electric field lines should never cross. Which point charge has the greatest field strength? Picturing an Electric Field Draw the electric field lines surrounding the positive and negative charge below. 183
Unequal opposite charges. Equal opposite charges. Equal positive charges. Draw the electric field around two equal negative charges. Draw the force on a test charge placed at various locations around the point charge. Allow students to choose. Draw the electric field around two unequal negative charges. Draw the electric field between two oppositely charged parallel conducting plates. Electric Fields for Equal Charges Electric Field for Unequal Charges 184
Scenario A + Scenario A + Show PE grav using a lump of clay. Scenario B B Electric Potential Energy How could you increase Fyou on charge the gravitational potential energy of a ball on d Earth? + A By doing work on it to increase its height from Earth s surface. E Scenario B + + + Fyou When on using charge opposite charges, can be treated like gravitational PE. d E Electrical Potential Energy potential energy associated with an object due to its position relative to a source of electric force. Consider the situation shown below. The negative charge created an electric field, E, around itself. Suppose you placed a small positive test charge, q, in the field at position A. It will experience a force in the direction of the field. In which scenario is the electric potential energy increasing? Explain. In Scenario A, because work is being done by an external force to pull the positive test charge away from the negative charge. The farther the test charge is from the negative charge, the more potential it has to move. Consider the following scenarios and the forces present. In which scenario does the test charge have the greatest potential energy? Is there always an electric potential difference between the two positions? Suppose you move the test charge in a circle around a negative charge. The force the electric field exerts on the test charge is always perpendicular to the direction you moved it, so you do no work. 185
E = \ F & V = Ed W q V= Fd q V = Electric Potential Difference in a Uniform Field q Toward E Opposite E + - This question is only PE PE valid for uniform electric fields. (point PE PE charges are not uniform) Potential Difference ( V ) difference in potential energy between two points. At which location will the test charge have more electric potential energy? A Which spot in general, A or B, is at a higher electric potential? Electric potential energy is dependent on the charge. Units J/C = Volt (V) AS WITH OTHER FORMS OF POTENTIAL ENERGY, IT IS THE DIFFERENCE IN ELECTRICAL POTENTIAL ENERGY THAT IS PHYSICALLY IMPORTANT. 1. If 21 joules of work is required to move 7.0 coulombs of charge between two plates, the potential difference between the two plates is W 21J V= = =3.0V q 7.0C 2. Two large, charged parallel plates are 4.0 cm apart. The potential difference between the two plates in 25 V. What work will you do to move a charge equal to that of one proton from the negative to the positive plate? W = qv = (1.60 x 10-19 C)(25 J/C) = 4.0 x 10-18 J 186
Repulsive force from positive plate a b c Electric Field Strength and Potential Difference between Two Parallel Plates Attractive force to negative plate 1000. V A positive test charge is placed at each of the three locations in the electric field: A, B, and C. a) At what location is the electrostatic force on the test charge the greatest? Draw in the electric field between the two parallel plates. Electrostatic force for a, b, and c are all same. b) At what location is the electric field strongest? E-field for a, b, and c are all same. c) At what location will the electric potential energy of the test charge be greatest? A (The electric potential increases in the direction opposite the electric field direction. That is, the electric potential is higher near the positively charged plate.) Draw and label a vector for the electric field and the force on the charged particle indicated. If a proton is placed as shown between plates that are separated by a distance of 3.5 cm with an electric field of 2.9 x 10 4 N/C. a) what is the force on the proton? F = Eq = (2.9x10 5 N/C)(1.60x10-19 C) = 4.6 x 10-15 N b) what is the acceleration of the proton? -15 F 4.6x10 N -27 m 1.67x10 kg a= = =2.8x10 m/s 12 2 c) how much work is done on the proton moving it to the bottom plate? W = qv = (1.60 x 10-19 C)(1000.v) = 1.6 x 10-16 J 187
+ + + + + + + electron + + proton neutron + + + + 1 + + ev + = + + 1.60 + + x 10-19 J Sketch the path of the particle moving with an initial velocity to the right through the electric field between the two parallel plates if the particle is a proton, an electron, a neutron. - - - - - - - - - - - - - - - - - - - - Which particle experiences a greater force? The electron and proton experience the greater force. A greater acceleration? The electron, because it has the smallest mass. The Electronvolt Electronvolt the energy that an electron (or proton) gains when accelerated through a potential difference of 1 Volt. A unit of energy commonly used in atomic and nuclear physics because of its convenient small size. Calculate the number of ev in 1.00 Joule. 6.25 x 10 18 1. A proton has 4.0 ev of work done on it as it moves in an electric field. How much energy in joules does the proton gain as the work is done? -19 æ1.60x10 J ö -19 4.0eV =6.4x10 J ç 1eV è ø 2. An electron falls through a potential difference of 30. Volts. How much kinetic energy does the electron gain? Express your answer in both joules and electronvolts. W = qv = (1.60 x 10-19 C)(30. V) = 4.8 x 10-18 J æ 1eV ö è1.6x10 J ø -18 4.8x10 J ç =30.eV -19 Volts are Joules / Coulomb 188