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Transcript
Electric Charge • Recall the 4 fundamental forces: – Strong, EM, Weak, Gravity • In order for the electromagnetic force to affect bodies the presence of charge is necessary. • Electric charge is an intrinsic characteristic of the particles that make up all matter. • Electrostatics is the study of stationary, or bound, charges. Moving charge is known as “current” and will be discussed later. • There are two known types of electric charge: – Positive charge and Negative charge • As a general rule, charges interact with one another by means of the electromagnetic force. • Like charges repel other like charges while opposite charges attract one another. Electric Charge • The fundamental unit of charge is called the Coulomb. Abbreviation: C • A particle carrying a single charge (positive or negative) carries a charge of 1.60 x 10-19 C • In physics, the variable used to signify charge is the lower-case letter q. Practice 1) A tennis ball is rubbed on the carpet. How many excess electrons are on the ball with a charge of -3.25 x 10-17 C? 2) A lightning bolt transfers about 9.7 x 1020 electrons to the earth. How much charge, in Coulombs, is transferred? Neutral Objects • Charge is a fundamental characteristic of all matter. • In the macro-scale world most objects are made of many atoms, each atom having multiple charge particles. • Like a single atom that has all its valence electrons same number of protons in nucleus as electrons in the outer shells, most large objects are considered neutral, having the same amount of positive and negative charge. Charging Objects (more on this later) • Objects can become “charged” by creating an imbalance of positive and negative charges on the objects. • While we often may describe an object as “positively charged,” please be aware that the presence of a positive charge is actually indicative of a lack of electrons, the absence of negative charges. Check out the three examples below. Conservation of Charge • Like energy, charge is always conserved despite changes to a system. This means if we start out with 3 positive charges and 2 negative in a closed system we must end up with the same amount of charge present in the system after any changes have occurred and been accounted for. • An object can only have a charge that is an integer multiple of the charge of an electron. • The only known exception to the rule above is for quarks, tiny sub-nucleonic particles that make up protons and neutrons. Extension • If a proton has a charge of 1+ and is made up of 3 quarks (2 identical “up” quarks and 1 “down” quark), why must quarks necessarily have fractional charges? • If a neutron has a net charge of zero and is made up of 2 down quarks and 1 up quark, can you figure out the charges on the up and down quarks? The material on this slide is an extension and will not be on your test. DON’T FREAK OUT! Conductors and Insulators • In the same manner as heat transfer, an electrical conductor is an object or material that can transfer electrical charge easily from one point to another. • An electrical insulator is an object or material that prevents the flow of electric charge. • Despite their inability to easily transfer charge from place to place, insulators can often become positively charged by stripping off electrons (or collect charge by accepting electrons). What kinds of materials are good electrical conductors? (in normal conditions) WHY??? 1) Metals 2) The metallic bond/crystal Conductors METALS Graphite impure water (contains ions) human body nerves plasma (hot ionized gas) Insulators pure water glass and ceramics plastic and rubber leather and fur paint and varnish paper and cardboard DRY gasses, including air vacuum stone and rock dry wood wax sulfur cloth Can you name some other conductors/insulators? Just b/c an object is made of insulating material does not mean that charge will not move through it, only that it is less likely. Metallic Bonds • Metallic bonds form by individual atoms of metallic substances which share all of their valence electrons. This phenomena creates what is called a “sea of electrons” in the material. • It is technically possible for an electron (a charged particle) to move from one end of an infinitely long strip of conductive material to the other end with no resistance. • There are few, if any, “conduction electrons” in the valence shell of an insulator. Charging by Conduction • Friction: We can utilize frictional forces to either deposit or removed electrons from different surfaces. – Rubbing a rubber rod with wool will result in the rod gaining a negative charge as the rubber has a tendency to “tear” electrons out of the wool. – Rubbing a glass rod with silk will result in the formation of a positive charge on the glass as the silk can actually remove electrons from the surface of the rod. Charging by Conduction • When a charged object (like a rubber rod) is placed in contact with a neutral conductor, the charges on the surface of the object are forced off onto the conductor. What do you think causes this to occur? hint: the answer has something to do with the electrostatic force!!! Conduct yourself well! –– – – – – –– – + – + – + – + +– + – + – + + – – Net charge rod after = ??? Net charge block after = ??? Charging by Induction • A charge is said to be induced when... • When a neutral object is brought into proximity (but not touching!) a charged object, the charges on the neutral object will spread out such that opposite charges will be attracted to the charge source and like charges will be repelled away from the source of charge. • If we can siphon off some of the repelled charges and then isolate the originally neutral body, the body now has a distinct charge. • One way to to this is with a “ground” Induced Polarization –– – – ––– – – + – + – + – + +– + – + – + + – – Grounding • To “ground” an object is simply to touch the object, either directly or by means of a conductive surface like a wire, to the earth. • The Earth, being infinitesimally large in comparison to all made made things, acts as an infinite repository of extra charge. • Thus if an object is highly negatively charged, the like charges on the object will repel each other, running through the grounding wire to the earth until a charge equilibrium (neutrality) is established on the object. Induction with grounding –– – – ––– – – + – + – + – + +– + – + – + + – – What causes the attraction & repulsion? • While modern science has some theories, they are young, relatively untested and well-beyond the scope of this course. • What we do know is that all charged bodies produce an electric field. This field is a type of force field (no joke!) that allows other charged particles to “feel” the presence of the charge producing the field. • Technically a “field” of any type is a potential to have a force, in this case, an electrostatic force. • The intensity of the electric field is given by the equation kq E 2 r where E is the intensity of the electric field, k is a constant, q is the size of the charge producing the field and r is the radial, or straight line, distance between the charge and the test point. • The intensity of the field is normalized (standardized) to measure the effect of the field per a single unit charge, also called a test charge. Electric Field Due To A Point Charge To draw an E-Field, select a point in nearby space to the charged Object. Mentally place a “test charge” at this point. Ask yourself, “How would this charge move due to the presence of the other charged body?” Field of an Electric Dipole Note the directions of the field lines. The E-Field variable is a vector quantity, since it is measured as reference to a test charge, which is always positive. The E-Field Variable • The E-Field variable measures the intensity of an electric field at some point in proximity to the field. • Symbol: E Units: C/m • The constant k – This value has to do with an Electric field’s ability to pass through space. For the problems we will work, it has a constant value of 8.99 x 109 Nm2/C2 • The amount of force is quantified by Coulomb’s Law of Electrostatic Force which we will discuss later. Quantifying the E-Static Force • Another way to define the electric field is by measuring the field’s effect, or force, on any concentration of charge, qo, placed in the field. This way we define the field as kq F E 2 r qo Where qo is the charge placed into the field and q is the charge creating the field. If we algebraically arrange this formula to solve for force, we see that F = Eqo. Expanding this equation, we end up with Coulomb’s Law for electrostatic forces. Coulomb’s Law Charge 1 F k Charge 2 q1 q 2 r 2 electrostatic constant 2 m k 8.99 109 N 2 4o C 1 2 C o 8.85 109 Nm 2 distance of separation LOOK FAMILIAR? Recall Newton’s Law of Universal Gravitation: m1m2 F G 2 r It’s really weird, yet fascinating and elegant how the universe works out such that two very different phenomena of nature are so similar at the most fundamental levels…this is one of many cases in physics where this symmetry stands out. BUT WAIT! They are NOT the same at all, and have no apparent relationship. One of the biggest failures of modern Physics is the inability to reconcile the 4 fundamental forces into a single causality. • Some consequences of Coulomb’s Law: – A shell of uniform charge attracts or repels a charged particle that is outside the shell as if the shell’s charge were concentrated at its center. – A shell of uniform charge exerts no electrostatic force on a charged particle that is located inside the shell. – On a conductor, any net, unbalanced charge will be found on the outside surface as a result of the electrostatic repulsion. *We will prove the top two statements in AP Physics C by means of the Gauss’s Law for electric fields. **The top two statements have corollaries in gravitation! Practice 1) A negative charge of -2.0 x 10-4 C and a positive charge of 8.0 x 10-4 C are separated by a distance of 0.30 m. What is the force between the charges? What direction will they move? 2) A negative charge of -6.0 x 10-6 C exerts an attractive force of 65 N on a second charge 0.050 m away. What is the magnitude of the second charge? 3) An object with charge +7.5 x 10-7 C is placed at the origin. The position of a second charge +1.5 x 10-7 C is varied continuously from 1.0 cm to 5.0 cm along the x-axis. Draw a graph of the force on the first charge. Wait, there’s more! 4) An object with charge +7.5 x 10-7 C is anchored at the origin. A second charge of -7.5 x 10-7 C is placed at coordinates (4,3) and allowed to move. Calculate the magnitude and direction (specify the angle) of the force on the second particle. 5) An object with charge +7.5 x 10-7 C is placed at the origin (it can move). Two charges, both of +1.4 x 10-3 C are anchored at x = +3 and x = -3 respectively. Find the force on the first charge. 6) What would happen if all three charges in 5) were allowed to move? What would happen if you revered the sign on the two outer particles to be negative? Storing Charge • A capacitor is a device which stores charge by using an unbalanced charge’s own electric field against it to hold it in place. • Capacitors are generally two pieces of conductive material placed close together but separated by an insulator. A CAPACITOR is two conductors separated by an insulator. If charges are placed on the conductors, then it stores electricity. It is important to note that the two conductors have EQUAL BUT OPPOSITE charges! In its simplest form, a capacitor is two parallel plate conductors separated by an air gap insulator. Capacitance Defined… • A capacitor stores charge by producing an electric field between the surfaces. This electric field “traps” charges on the plates of the capacitor. • The dimensions and material that comprises the capacitor will determine how much charge can be stored by the capacitor. • The variable C, or capacitance, defines how much charge can be stored on the capacitor. Charge stored on the capacitor Capacitance q C V Units: charge per electric potential or Coulomb per Volt, C/V. Electric Potential between the opposing surfaces of the capacitor. Uh oh…another variable… • Every E-Field has an electric potential associated with it. The electric potential is the sum of all electric fields through a particular area. Defined another way, the Efield is the rate which the electric potential changes across space. For you calculus people that’s E = dV/dx Electric Field inside a capacitor (or other area of uniform field) • Using the equation from the previous slide, if the field is changing at a uniform rate this equation becomes a very useful and easy one: V = Ed For many capacitors this equation describes the electric field in between the metal surfaces. • Generally, we speak of just the electric potential (V) of an E-Field. It can be conceptually defined as the amount of work that the field does on a particular amount of charge, qo. • This would be kind of like defining GPE without mass. (i.e., mgh/m, meaning GPE per unit of mass). Electric Potential W V qo • Symbol: V Units: Volts (V) • Electric potential of a point charge q: kq V r For many point charges in an array kq V r However, the sign of the charge must be taken into account when calculating the electric potential. So it is possible to have a positive potential or a negative potential overall, or even a net zero potential. Other topics you need to know: (a.k.a. you should look these things up on the interwebs) • Faraday Cage • Lyden (or Leyden) Jar • Miliken’s Oil Drop Experiment – What was the main idea and setup? What did Miliken accomplish? • Lightning rods and building up charge on a point on a conductor – Since charge accumulates on the outside of all conductors, any sharp corner will have a large concentration of charge (and a higher absolute V) than any smooth surface.