PHYSICS - Electrostatics

Electrostatics, or electricity at rest, involves electric charges, the forces between them, and their behavior in materials.

22.1 Electrical Forces and Charges The fundamental rule at the base of all electrical phenomena is that like charges repel and opposite charges attract.

22.1 Electrical Forces and Charges The helium nucleus is composed of two protons and two neutrons. The positively charged protons attract two negative electrons.

22.1 Electrical Forces and Charges

22.2 Conservation of Charge An object that has unequal numbers of electrons and protons is electrically charged.

22.2 Conservation of Charge A charged atom is called an ion. A positive ion has a net positive charge; it has lost one or more electrons. A negative ion has a net negative charge; it has gained one or more extra electrons.

22.2 Conservation of Charge Innermost electrons tightly bound to the nucleus. Outermost electrons are bound very loosely. How much energy is required to tear an electron away from an atom varies for different substances.

22.2 Conservation of Charge When electrons are transferred from the fur to the rod, the rod becomes negatively charged.

22.2 Conservation of Charge Electric Charge is Quantized Any object that is electrically charged has an excess or deficiency of some whole number of electrons. This means that the charge of the object is a wholenumber multiple of the charge of an electron.

22.2 Conservation of Charge Electrons are neither created nor destroyed but are simply transferred from one material to another. This principle is known as conservation of charge.

22.2 Check Question If you scuff electrons onto your shoes while walking across a rug, are you negatively or positively charged?

22.3 Coulomb s Law Coulomb s law states that (for charged particles or objects that are small compared with the distance between them), the force between the charges varies directly as the product of the charges and inversely as the square of the distance between them.

22.3 Coulomb s Law Recall from Newton s law of gravitation...

22.3 Coulomb s Law For charged objects... Where: d is the distance between the charged particles. q 1 represents the quantity of charge of one particle. q 2 is the quantity of charge of the other particle. k is the proportionality constant.

22.3 Coulomb s Law The SI unit of charge is the coulomb, abbreviated C. A charge of 1 C is the charge of 6.24 10 18 electrons.

22.3 Coulomb s Law The Electrical Proportionality Constant The proportionality constant k in Coulomb s law is similar to G in Newton s law of gravitation. k = 9,000,000,000 N m 2 /C 2 or 9.0 10 9 N m 2 /C 2

22.3 Coulomb s Law

22.3 Coulomb s Law Because most objects have almost exactly equal numbers of electrons and protons, electrical forces usually balance out. Between Earth and the moon, for example, there is no measurable electrical force. In general, the weak gravitational force, which only attracts, is the predominant force between astronomical bodies.

22.4 Conductors and Insulators Materials through which electric charge can flow are called conductors. Metals are good conductors for the motion of electric charges because their electrons are loose.

22.4 Conductors and Insulators Electrons in other materials rubber and glass, for example are tightly bound and remain with particular atoms. They are not free to wander about to other atoms in the material. These materials, known as insulators, are poor conductors of electricity.

22.4 Conductors and Insulators In power lines, charge flows much more easily through hundreds of kilometers of metal wire than through the few centimeters of insulating material that separates the wire from the supporting tower.

22.4 Conductors and Insulators Semiconductors are materials that can be made to behave sometimes as insulators and sometimes as conductors.

22.4 Conductors and Insulators Superconductors are materials that at certain low temperatures acquire zero resistance to the flow of charge.

22.5 Charging by Friction and Contact Two ways electric charge can be transferred are by friction by contact

22.5 Charging by Friction and Contact Electrons can be transferred from one material to another by simply touching. When a charged rod is placed in contact with a neutral object, some charge will transfer to the neutral object. This method of charging is called charging by contact.

22.6 Charging by Induction If a charged object is brought near a conducting surface, even without physical contact, electrons will move in the conducting surface. This is called charging by induction.

22.6 Charging by Induction

22.6 Charging by Induction The charge on the spheres has been redistributed, or induced.

22.6 Charging by Induction

22.6 Charging by Induction Charge Induction by Grounding

22.6 Charging by Induction When we touch the metal surface with a finger, charges that repel each other have a conducting path to a practically infinite reservoir for electric charge the ground. When we allow charges to move off (or onto) a conductor by touching it, we are grounding it.

22.6 Charging by Induction Charging by induction occurs during thunderstorms.

22.6 Charging by Induction Lightening Rods The primary purpose of the lightning rod is to prevent a lightning discharge from occurring. If lightning does strike, it may be attracted to the rod and shortcircuited to the ground, sparing the building.

How an Electrophorus Works

22.7 Charge Polarization Charge polarization can occur in insulators that are near a charged object.

22.7 Charge Polarization a. When an external negative charge is brought closer from the left, the charges within a neutral atom or molecule rearrange.

22.7 Charge Polarization a. When an external negative charge is brought closer from the left, the charges within a neutral atom or molecule rearrange. b. All the atoms or molecules near the surface of the insulator become electrically polarized.

22.7 Charge Polarization

22.7 Charge Polarization Electric Dipoles Many molecules H 2 O, for example have a little more negative charge on one side of the molecule than on the other. Such molecules are said to be electric dipoles.

22.7 Charge Polarization In summary, objects are electrically charged in three ways. By friction, when electrons are transferred by friction from one object to another. By contact, when electrons are transferred from one object to another by direct contact without rubbing. By induction, when electrons are caused to gather or disperse by the presence of nearby charge without physical contact.

22.8 Electric Fields You can sense the force field that surrounds a charged Van de Graaff generator.

22.8 Electric Fields The distance between field lines indicates magnitudes. g

22.8 Electric Fields F G F G = mg

22.9 Electric Field Lines E E

22.8 Electric Fields F G F E F G = mg F E = qe

22.8 Electric Fields The direction of an electric field at any point, by convention, is the direction of the electrical force on a small positive test charge placed at that point.

22.9 Electric Field Lines a. The field lines around a single positive charge extend to infinity.

22.9 Electric Field Lines a. The field lines around a single positive charge extend to infinity. b. For a pair of equal but opposite charges, the field lines emanate from the positive charge and terminate on the negative charge.

22.9 Uniform Electric Fields + + + + + + + + + E - - - - - - - - - Between two parallel plates containing equal but opposite charges, the electric field is uniform. Both the magnitude and direction of the field is the same at all points between the plates.

22.9 Uniform Electric Fields + + + + + + + + + q + F E F E - - - - - - - - - - q E F E = qe

22.9 Example Robert Millikan determined the charge on an electron by suspending negatively charged oil drops in a uniform electric field created by two charged plates. Determine the charge on the oil drop in terms of its mass (m), the electric field (E) and the gravity of Earth (g). + + + + + + + + + F E oil drop - F G - - - - - - - - -

22.9 Example When an electron is released from rest in a uniform electric field E, it reaches a velocity of v after traveling a distance of x. In terms of v, what will be the electron s velocity if the magnitude of the electric field is doubled while traveling the same distance?

22.9 Electric Fields of Point Charges So far we have two equations for the electrical force: F E = qe AND As with gravity, we can set these equal to each other and solve for E to determine the strength of the electric field at a given position. The result should look very familiar from our study of gravity...

22.9 Electric Fields of Point Charges

22.9 Example A conducting sphere contains a charge q. The electric field at a set distance from the center of the sphere is E. If the charge on the sphere and the distance from the sphere are both doubled, by what factor would the electric field change?

22.9 Superposition of Electrical Fields A +8 coulomb charge is located 2 meters to the left of the origin. A -4 coulomb charge is located 2 meters to the right of the origin. Determine the magnitude and direction of the electric field at point P located at the origin. 8 C P 4C + - -2-1 0 1 2

22.9 Superposition of Electrical Fields Two negative charges, 4 coulombs and 16 coulombs, are separated by a distance of 1 meter. Determine the location, as measured from the 4-coulomb charge, where the electric field is zero. 4 C 16C - - 1 meter

22.10 Electric Shielding

22.10 Electric Shielding Consider a charged metal sphere. Because of repulsion, electrons spread as far apart as possible, uniformly over the surface. A positive test charge located exactly in the middle of the sphere would feel no force. The net force on a test charge would be zero.

22.10 Electric Shielding

22.10 Electric Shielding How to Shield an Electric Field There is no way to shield gravity, because gravity only attracts. Shielding electric fields, however, is quite simple. Surround yourself or whatever you wish to shield with a conducting surface. Put this surface in an electric field of whatever field strength. The free charges in the conducting surface will arrange on the surface of the conductor so that fields inside cancel.

22.11 Electrical Potential Energy

22.11 Electrical Potential Energy Imagine moving multiple charges from A to B. For each charge we move, there is a gain in PE. So it makes sense to talk about difference in potential energy per charge.

22.11 Electrical Potential Energy Difference in potential energy per charge POTENTIAL DIFFERENCE ELECTRIC POTENTIAL VOLTAGE

22.11 Electrical Potential Energy Difference in potential energy per charge Joules Coulomb 1 Joule / Coulomb = 1 Volt

22.11 Electrical Potential Energy

22.11 Electrical Potential Energy V = Ed E = V d CAUTION: This equation is only for uniform electric fields. For example, for the field between two parallel charged plates.

22.12 Electric Potential Electric potential is not the same as electrical potential energy. Electric potential is electrical potential energy per charge.

22.12 Electric Potential

22.12 Electric Potential If there were twice as much charge on one of the objects, would the electrical potential energy be the same or would it be twice as great? Would the electric potential be the same or would it be twice as great?

22.12 Example + + + + + 6 V P + - 4 V d 2 V - - - - - - 0 V

22.12 Example Two charged plates with a 20 newton per coulomb electric field are separated by a distance of 10 centimeters. A proton is located at the midpoint between the plates. A) Determine the potential difference between the charged plates. B) Determine the potential acting on the proton.

22.12 Potential of Point Charges E 4 V 2 V V = kq r 6 V +q E = kq r 2

22.12 Example A +4 coulomb charge is located 4 meters to the left of the origin. A -4 coulomb charge is located 4 meters to the right of the origin. Determine the electric potential at point P located at the origin.

22.12 Electric Potential Energy Once we know the electric potential of a point in space, it s easy to find the electric potential energy of any amount of charge. Since V is simply difference in potential energy PER CHARGE, we only need to multiply by how much charge we have to find the total potential energy. U E = qv

22.12 Work of Electricity W E = ΔK = -ΔU E = -qδv = -q (V f - V i ) W = q (V f - V i )

22.12 Example B + A -4 V -2 V 0 V 2 V 4 V 6 V The diagram above shows the equipotential lines in a region of space. Determine the work done on a 2- coulomb charge that is moved from point A to point B.

22.12 Conservation of Energy Don t forget that you can still apply what you already know about energy to solve electric potential problems. See below: - - - - + + + Two charged plates have a potential difference of V. An electron of mass m and charge e is initially at the negative plate. It accelerates through the potential difference. Determine the electron s max speed, v, in terms of the given variables.

22.13 Electrical Energy Storage A capacitor is a device that can store electrical energy.

22.13 Electrical Energy Storage

22.13 Capacitance Capacitance, C, is measured in farads (F) and is a measure of the ability of a capacitor to store charge and energy. Capacitance is proportional to the area of one of the plates, A and inversely proportional to the distance of the plate separation, d. Epsilon is a constant known as the permittivity of free space and = 8.85 x 10-12 C 2 /Nm 2

22.13 Capacitance Other formulas you might need for capacitance:

22.13 Capacitance Other formulas you might need for capacitance: U C =

22.14 The Van de Graaff Generator