CHAPTER 16Electric Forces and Electric FieldsElectric Charge: Atoms are made of equal numbers of protons (positive charge) and electrons (negative charge) We say something is electrically charged if it contains unequal amounts of positive and negative charge In this class (as was the case in chemistry) objects become charged by gaining or losing electrons. They do not gain or lose protons.

Observations Regarding Charge Like charges (or charged objects) repel each other Unlike charges (or charged objects) attract each other We can positively charge an object by removing some electronsand We can negatively charge an object by adding some electrons Charge is conserved. If an object becomes positively charged, then some other object (s) must have become negatively charged Charge comes in discrete amounts.Every proton has the exact amount of positive charge as every other protonEvery electron has a similar amount of negative chargeTrivia Question:Who decided that protons have positive charge and electrons have negative charge?Ben Franklin

Terms:Insulator:Material that does not allow electrons to freely flow through it (Ex: plastic, rubber, glass)Conductor:Material that does allow electrons to freely flow through it (Ex: metals)How does an object obtain a net charge (uneven amounts of protons and electrons)? It always either gains or loses electrons. Protons never move to or from an object under normal conditions. Ways to transfer electronsFriction Conduction Induction (Ex: the shock you feel when you touch your car after you have just driven it)(Ex: direct contact with a charged object)(Ex: obtaining a charge due to the influence of nearby charged object

Charging by Conduction

Charging by Induction

Charged Particle Brought Near Uncharged ConductorAttractive Forces Result

Charged Particle Brought Near Uncharged ConductorAttractive Forces Result

Electric Force (Fe)q1q2r2Question:How do you change a proportionality into an equality?Answer:Add a proportionality constant.Fe = Newtonsq1 = coulombs of chargeq2 = coulombs of charger = distance between centers of charged objectsk = 9.0x109 Nm2/C2Coulomb is new basic unit (m, s, kg, C)+1 coulomb = charge of 6.3 x 1018 protons

Example Problem (Coulombs Law Application)Determine Fe and Fg between a hydrogen atom proton and its orbiting electron (r = .53x10-10 m)a) Fe part: q1 = proton = 1 / 6.3x1018Cq1 = 1.6x10-19Cq2 = electron = -1.6x10-19Cgood # to rememberFe = 8.2 x 10-8 Nb) Fg part:Fg = 3.6 x 10-47 NFe/Fg = 2.3 x 1039Fe is much larger force than Fg

Electric FieldsCharged particles exert a force on other charged particles (Fe) just like massive objects exert a force on other massive objects (Fg).Field lines are used to show the strength and direction of the electric field (E) field lines point in the direction that a small positive test charge would move if placed in the field. like charges repel. Unlike charges attract field lines never cross. Why? closer lines indicate stronger fields field lines are a way humans visualize something we cannot sense. Field lines are only a model.

Field is 3-dimensional, not 2. Lines spread out through ever increasing spheres surrounding the charge. Area of sphere = 4r2Example: 12 field lines:Distance from charge (m)1.02.03.0rApproximate Surface Area (m2)12 m248 m2108 m2Strength of field (lines/m2)12/1212/4812/108 1 1/22Field strength proportional to 1/r2 1/32 1/r2

Electric Force (Fe)Gravitational Force (Fg)Proportional to product of chargesProportional to product of massesProportional to inverse of distance squaredProportional to inverse of distance squaredFe = E1 q2Fg = g1 m2E1 = electric field caused by object 1 (N/C)g1 = gravitational fieldcaused by object 1 (N/kg) or (m/s2)E and gNot forcesAre vectorsSimilar conceptsDifferent units

Superposition (Addition of E-fields)Example Problem: (Point between 2 charges)Calculate E1 at PE1 = 5.6x108 N/C (left)A second charge is placed in the vicinity of P. Calculate E2 at P.E2 = 7.0x107 N/C (left)ET (at P) = E1 + E2ET = 6.3 x108 N/C (left)

Electrostatics with Conductors in EquilibriumIn Equilibrium:Charges are not moving.Conductors:Materials that contain charges (electrons) that are not bound to any atom and are free to move about within the material.For a conductor in electrostatic equilibrium:1. The electric field is zero everywhere inside the conductor.2. Excess charge resides entirely on the surface of the conductor.Reasoning:Repulsive forces cause charges to distance themselves from each other causing them to migrate to the surface.Reasoning:If an E-field did exist, then electrons would move and in the static condition they are not moving. Hence, there must not be an E-field inside the conductor.

3. The electric field outside a charged conductor is perpendicular to the surface.Reasoning:If this were not the case (as shown), a component of the E-field vector parallel to the surface would cause the charge to move. However, the charge is not moving (static equilibrium) and so the E-field must be perpendicular to the surface.4. Excess charge tends to accumulate at sharp points on the surface.

Work is being done in two places. Can you name them?Positive charge is sprayed onto the moving belt at point A. (Actually, electrons are pulled off the belt onto an electrode.)Charge moves up the rotating belt and is scraped off by a wire brush at point B. (Actually, electrons move onto the belt from the sphere.)Positive charge builds up on the sphere and spreads itself out on the sphere exterior surface.At some point the resulting E-field becomes strong enough to ionize air and charge leaks off to the air.

*Self explanatory slide.*3. For example, a sodium atom contains 11 positively charged protons and 11 negatively charged electrons. The sum of the charges is zero (+11 + -11 = 0). The 11 positively charged protons are deep inside the atom and locked strongly together with each other and with some neutrons in the nucleus of the atom. A proton is very difficult to remove from a nucleus and we shall assume for now that they CANNOT be removed. However, the negatively charged electrons are not tightly bound to each other or to the nucleus and can be removed. If one is removed, then the sodium atom will become a sodium ion with a charge of +1 (+11 + -10 = +1).

The electron must go somewhere and is often attached to another atom such as chlorine. That atom will gain one extra negative charge and will have a charge of -1.

6. The designation of positive for protons and negative for electrons is absolutely arbitrary. That is, one could just as easily designated the electrons as being positively charged and the protons being negatively charges. In fact, positive and negative are arbitrary distinctions themselves. The words simply denote that some feature, charge, that exists in the proton in one form exists in the electron in an opposite form.*Self-explanatory slide.*1. A charged object such as the charged rubber rod shown in this slide can charge an uncharged conductor simply by coming into direct contact with it. *1. A charged object such as the negatively charged rubber rod shown in this slide can cause an uncharged conductor to acquire a charge. The negatively charged rod is first brought near the conductor. This causes electrons in the conductor to migrate away from the rod. The right (negatively charged side of the conductor) is then grounded. Grounding simply means to come in contact with a large neutrally charged object such as the Earth (the ground). This causes the negatively charged side of the conductor to lose electrons to the ground and once again become neutral. However, the other side of the conductor still has a positive charge. When the rod is removed from the vicinity of the conductor, the excess positive charge on the conductor spreads out over the entire conductor.*4. As the positively charged particle and the uncharged conductor are brought near each other some of the electrons in the conductor migrate towards the positively charged particle (electrons are free to move about in a conductor). The protons in the conductor DO NOT move about the conductor. Protons exist in the nucleus of each atom and are fixed in place.

6. Think of the conductor as having two sides. The side closest to the positively charged particle obeys Coulombs Law and an attractive force results. The other side of the conductor obeys Coulombs Law and a repulsive force results. However, since the distance between the negative side of the conductor and the positive charge is less than the distance between the positive side of the conductor and the positive charge, the attractive force is greater than the repulsive force and a net attractive force results.

*6. For similar reasons as mentioned in the previous slide, an attractive force also results when an uncharged conductor is brought near a negatively charged particle. Therefore, you cannot tell of a charged particle is positively or negatively charged simply by the way an uncharged conductor behaves when brought near it.

*5. The electric force caused by a charged particle acting on another charged particle is totally analogous to the gravitational force where a force is caused by a particle with mass acting on another particle with mass. Both forces are inversely proportional to the square of the distance from the centers of the particles. And both are proportional to the product of the attribute of interest. In the case of gravity, the force is proportional to the product of the particles masses. In the case of the electric force, the force is proportional to the product of the particles charges. In both cases we change a proportional relationship to an equality by the use of a proportionality constant. In the case of the force of gravity, the proportionality constant is the Universal Gravitational Constant, G. In the case of the electric force, the proportionality constant is k, Coulombs Constant. It is named after Charles Coulomb who is credited with discovering this relationship.

9. Since the start of this course we have worked with only 3 fundamental units; meters, seconds, and kilograms corresponding to length, time and mass measurements. We now introduce a forth basic unit, the Coulomb. The Coulomb is an amount of charge and this unit is abbreviated with a capital C. 1 C of positive charge is equal to charge associated with 6.3 x 1018 protons.1 C of negative charge is equal to the charge associated with an equal amount of electrons. 1 Coulomb of charge is a lot of charge. In this chapter we will work with milli-coulombs (mC), micro-coulombs (C), and nano-coulombs (nC). These are respectively 10-3, 10-6, and 10-9 coulombs.*1. This problem is meant to illustrate the relative size of the gravitational and electric forces acting on a single proton and single electron making up a single hydrogen atom.

15. While both forces could be considered small, the electric force of attraction is 2.3 x 1039 times as great as the gravitational force of attraction. This is a huge difference of almost unimaginable size. The electric force is a thousand trillion trillion trillion times the size of the gravitational force. For this reason, we often ignore gravitational effects when dealing with charged particles. *9. Field lines, either gravitational or electric are a way of visualizing something we cannot see. The field line model is actually a 3-dimensional model. However, paper only allows us to write in 2-dimensions.

Try to envision field lines for the positive changed particle coming out of the particle evenly spaced and pointed in all directions.

The field is stronger closer to the charged particle and in fact the field lines get very close together at the surface of the charged particle.

For the negatively charged particle we point the field lines toward the charge rather than away from it. The direction of the field lines is the direction that a small positive charge would move if placed in the field. Since like charges repel each other, a small positive charge placed near the positively charged particle would move away from it. That is why the field lines point away from a positively charged particle. Oppositely charged particles are attracted to each other. Therefore a small positive charge placed near the negatively charged particle would move towards it. That is why the field line point towards a negatively charged particle.*19. Try to imagine a spherical surface surrounding the charged particle some distance from the charged particle. The field lines will be going through the spherical surface. The closeness of these lines as they go through the spherical surface gives some measure of the strength of the field at this distance from the charged particle. In this example I am using 12 field lines. This is again an arbitrary number. However, once I have chose this number I would want to use 24 lines for a particle with twice the charge and 6 lines for a particle with have the charge.

At 1 meter from the charged particle a spherical surface surrounding the particle would have a surface area of approximately 12 square meters (area of sphere = 4r2). This results in a field line density of approximately 1 field line per square meter.

At 2 meters from the charged particle a spherical surface surrounding the particle would have a surface area of approximately 48 square meters. This results in a field line density of approximately 1/4 field line per square meter.

At 3 meters from the charged particle a spherical surface surrounding the particle would have a surface area of approximately 108 square meters. This results in a field line density of approximately 1/9 field line per square meter.

The field line model predicts what we actually measure. That is, the strength of the electric field is inversely proportional to the square of the distance from the charged particle.*Self-explanatory comparison of electric and gravitational forces.*1. Two charges located near each other each create their own electric field. The field strength and direction at a specific location relative to the charge is a vector, E. The electric field at a location influenced by both charged particles can be found by adding the vectors E1 and E2 associated with the two charged particles.

12. In this situation the point of interest, P, is located on a line between the two charges. The electric field, E1, points toward the negatively charged particle q1 and the magnitude of E1 is easily calculated. The electric field, E2, points away from the positively charged particle q2 and its magnitude is also easily calculated.

14. Since E1 and E2 point in the same direction, it is easy to add these vectors. Simply add their magnitudes and point the resultant vector in the same direction as the individual vectors.*Self Explanatory slide.

*Self explanatory slide.

*Self Explanatory Slide.