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A Review of Basic Atomic Structure & Terms Atom – smallest piece of any element that still has the properties of that element electrically neutral: # of protons = # of electrons Atomic number - # of protons in an atom Determines what element it is. Atomic mass essentially tells how many protons and neutrons an atom has, but it’s rarely a whole number because most elements have isotopes Isotope – versions of the same element containing different numbers of neutrons in the nucleus Ions – a charged atom Positive ion – more p+ than e-, so lost electrons Negative ion – more e- than p+, so gained electrons A Review of Basic Atomic Structure & Terms Basic atomic structure : particle symbol location mass (kg) Charge (C) proton p+ nucleus 1.673 x 10-27 e = +1.602 x 10-19 electron e- electron cloud 9.11 x 10-31 e = - 1.602 x 10-19 neutron n0 nucleus 1.675 x 10-27 0 YUCK!! Almost beyond comprehension, the nucleus is incredibly small & dense, while the electrons are incredibly rare & far out! The protons are tightly held in the nucleus by the Strong Nuclear force (one of the 4 fundamental forces) and so it takes a nuclear change (aka nuclear reaction – examples: fission or fusion) to change the number of protons in an atom! But the electrons are WAY out there… often easily swiped away by even just the brush of a hand… Electrostatics and Basic Behavior Electrostatics is the study of static electricity ► electro refers to electric charge the charge subatomic particles have… (e-, p+) ► static means ‘at rest’ as opposed to moving, which is called current electricity (Ch 18…) Like charges repel; opposite charges attract… with a force determined by Coulomb’s Law. Law of Conservation of Electric Charge: While charge can be moved from one place/object to another, the total amount of electric charge will remain the same… charge can’t be created or destroyed. Insulators vs Conductors Conductors: Insulators: electrons flows freely almost no electrons flow due to low electron affinity due to high electron affinity Ex: metals, water Ex: plastics, glass, wood 3 Ways to Charge an Object ► Charging by Friction: rub 2 neutral objects together. If they’re different electron affinities, one will give up e’s becoming positive and the other will grab the extra e’s becoming negative. Ex: static cling in laundry or with clothes/hair plastic slides at a park playground water particles/clouds in a thunderstorm ► Chg by Contact: touch charged object to a neutral one The excess charge will be looking to repel farther away and so the neutral one’s surface becomes a great place to do that – it ends up charged as well, with the same charge as the originally charged object. Ex: metal leaves on an electroscope if you’re charged (by friction typically), then you touch (shock) something 3 Ways to Charge an Object ► Charging by Induction (aka induced charge separation): bring a charged object near (don’t touch them) to a neutral one and the charges on the neutral one will separate. The “like” charges move away from the originally charged object, leaving the neutral object with a positive side and a negative side Ex: electroscope again rod sways stream of water due polar molecules in H2O during a thunderstorm… the set up for lightning to strike the ground 1 Way to Discharge an Object ► Grounding: Connect it, either directly, or by means of a conducting material, to the massive Earth which is capable of accepting a lot of excess charge, but not becoming charged itself. Ex: lightning rod a shock from a anything (doorknob, person, etc) on a dry day dangling wire from car/wheelchair 3rd prong or polarized plugs Examples of Electrostatics: Photocopy Machines Photocopy machine: • drum is charged positively • image is focused on drum • only black areas stay charged and therefore attract toner particles • image is transferred to paper and sealed by heat Example of Electrostatics: Computer Printers Laser printer is similar, except a computer controls the laser intensity to form the image on the drum Coulomb’s Law Name after French Charles Coulomb; published in 1785: Coulomb’s Law is the mathematical relationship that is used to determine the strength of the electric force (Fe) between 2 charged particles (q) or objects. Extremely similar to Newton’s Universal Law of G! (p507) NUL of G ► Any 2 masses attract CL for Electric Charges ► Any 2 charges attract or repel! ► FG = Gm1m2/r2 ► Fe = k q1q2/r2 ► Remember inverse square? ► So inverse square as well ► G = 6.67 x 10-11 Nm2/kg2 ► k = 9.0 x 109 Nm2/C2 That’s a huge difference between constant values!! k ≈ 1020 bigger than G That’s why… ► hair can stick up with balloon or sweater ► socks hang onto each other out of the dryer ► refrigerator magnets stay up on the frig door Correct interpretation of these phenomena: The Fg of the entire Earth is weaker than the Fe of the tiny charged particles (p’s & e’s) on these objects! We don’t hear much about Fe, even though it’s so much stronger than Fg, because most objects are electrically neutral, so Fe = 0, but objects always have mass, so there’s always Fg. But at the atomic/molecular level, it’s responsible for all the forces we’ve studied so far, except gravity! all contact forces (pushes & pulls) normal force friction elastic A few additional notes on Fe = kq1q2/r2 charges (q’s) must be small relative to the distance between them – called point charges ► q is the quantity of charge present on an object units are Coulombs (C) Charge is quantized – smallest amt possible called elementary charge – the amt of a single e- or p+: ► qe = -1.6 x 10-19 C & qp = +1.6 x 10-19 C ► So then 1 Coulomb of charge has 6.25 x 1018 individual charges in it! If q’s are the oppositely charged, then Fe is an attractive force If q’s are similarly charged, then Fe is a repulsive force ► Superposition for Electric Charges Principle of Superposition: for multiple point charges, the forces on each charge, from every other charge, can be calculated and then added as vectors. ► The net force on a charge is the vector sum of all the forces acting on it. Fon q = 1Fq + 2Fq +3Fq + … 1st: find F between each set of charges, using Coulomb’s law. 2nd: add up those F’s using vector addition techniques. Review of Vector Addition (a) original vectors to be added (b) adding them tip to tail (c) adding them by parallelogram (d) adding them by components Electric Fields Force fields – the space around an object where that object is able to apply a “force-at-a-distance”. ► Used to explain the problem of forces being applied without contact – started with Newton’s UL of G. ► Idea from Michael Faraday in mid 1800’s ► Examples: gravity, electric, magnetic ► Understood now as not real, just an easy way to picture Einstein’s curved space idea. ► This space reaches out infinitely far in theory, ► but in practice, it’s strength falls by ISL. ► Electric Fields (all fields) are vector quantities Understanding Electric Fields The electric field is defined as the force acting on a small charge, divided by the amount of that charge: E = Fe/q(2) Units: Newtons / Coulomb Where q2 represents the charge of a test charge… which refers to a small amount of (positive) charge, relative to q1 (the charge creating the field) that it won’t disturb/affect the field it’s located in. But really, a test charge is a concept, we don’t actually need to have a q placed there… And E doesn’t depend on the mag of q2, because however you change q2, Fe will change proportional… by Coulomb’s law… Understanding Electric Fields Before you think you’re very confused, you’ve actually seen this before!! Think back to gravity, the other “field” we’ve covered: recall Fg = mg for weight, right? then rearrange to g = Fg/m … If you doubled m, would that change g?? NO! Because Fg would change proportionately, so g is the constant, created by the “main” mass creating the field, at a particular location. So really, g can be thought of as “gravitation field strength”, instead of just acceleration due to gravity, where g can be found by taking the force of gravity, Fg, per amount of mass, m, that’s located in the field, at that location. Well, that’s what E is for charges…. Understanding Electric Fields Let’s go back to the two masses in Universal Gravitation: Remember how Fg = FG on the surface of a planet and m?g = Gm1m2/r2 so g = Gm1/r2 ?? This means m2 doesn’t affect the value of g, but m1 does! It’s the same for the two charges in Coulomb’s Law: Fe = Fe (just for continuity with above) and q?E = kq1q2/r2 near a point charge so E = kq1/r2 !! So E is a measure of the effect of the charge creating the field at that location, unaffected by the test charge placed at that location. Math of Electric Fields So now we have two equations that deal with E… 1st, the definition of all electric fields, no matter the shape of the charge creating them: E = Fe/q (comparable to g = Fg/m) where this q is the one in the field, and it won’t alter the value of E, but can be used to determine E, if we know the amount of force acting on q. 2nd, the equation for E created by a point charge: E = kq/r2 (comparable to g = Gm/r2 ) where here we see E is a measure of the effect of the charge creating the field at that location, unaffected by the test charge placed at that location. So it’s really important to remember which q is which in each equation!! Both of them find E in units of Newtons/Coulomb or N/C. Math of Electric Fields Based on E = Fe/q: ► if q(2) is positive, E & F are in the same direction, ► if q is negative, E & F are in opposite directions. But this is confusing… If we used our “mechanics” way to show electric force around a point charge, it would look like this: And we haven’t even represented the electric field yet. This could get very confusing, so instead we use… Electric Fields Lines Recall vectors can be represented by arrows of a particular length, pointing in a particular direction. That has worked great up until now, but physicists came up with a more practical and useful way to indicate the strength and direction of fields: Direction: always points to where the positive test charge would go if released at that point in the field. So in a field created by ►a negative charge, that’s into the charge, ►a positive charge, that’s away from the charge. Instead of length to represent strength of field, we use concentration of lines – the number in a given area. Their length, then, can be left as infinitely long to indicate the size of the field. Electric Field Lines about a Point Charge ► The lines are infinite ► Arrows placed on them show the direction of the test charge if placed in the field at that point. ► Fewer lines in the same amount of space in the left picture indicates less field strength than the picture on the right with a greater concentration of lines. ► There’s still field between the lines, empty space is just to represent relative strength. ► They’re also 3D! But that’s hard to draw on flat paper. Electric Field Lines about Point Charges ► Notice the curvature of the field lines of the electric dipole. That’s from the vector addition of two fields acting at the same location. ► This means E acts tangent to the line, if in fact the lines are curved. ► If one of these charges disappeared, the lines around the other would be straight again. ► These curves still map out the path of a test charge if placed in this field. ► They will never cross: E has only one single direction at any particular location… If they crossed, that would indicate two possible directions. Electric Field between Parallel Plates There are actually many uses for oppositely charged parallel plates in everyday life – The most common of which is in a capacitor, which we’ll learn more about in Ch 17. Note, as long as the size of the plates is large compared to the separation distance between them, then the value of the E is a constant, as shown by the equally spaced, parallel electric field lines. The equation to determine it is: E = 4kq/A A is area of one plate q is the magnitude of charge on each plate Electric Shielding Using an encasement (box, cage, cover wrap) made of a conductor (metal) to protect (shield) anything (delicate electronics, you…) from the effects of charge. Because the repulsive forces between charges cause them to spread out over the surface of a conductor in such a way as to cancel each other’s field inside the conductor. The electric field inside an electric shielding device is always zero – naturally – the charges don’t come to rest until it is. Often referred to as a Faraday’s Cage… Electric Shielding Ex: coaxial cable TV/DVD/cable electric guitars your car in an electrical storm an airplane too To obtain this zero field strength, charges congregate on points and corners of various shapes. A Different, More Fundamental, Constant than k… ► A Glimpse to the Future… Maxwell’s Equations When/If you study E&M in college, you’ll get right into Maxwell’s equations, named after James Clark Maxwell, who published them in 1861. (He is also credited with 1st suggesting that light is an electromagnetic phenomenon.) They are a set of partial differential (calculus) equations that, together with the Lorenz Force law, form the foundation of classical electrodynamics, classical optics, and electrical circuits. These areas of physics are the basis for all electric, optical and radio technologies like power generation, electric motors, wireless communication, cameras, televisions, computers etc. Maxwell's equations describe how electric and magnetic fields are generated by moving charges, and changes of each other. One important consequence of the equations is that fluctuating electric and magnetic fields can propagate at the speed of light, and this electromagnet radiation manifests itself in many ways from radio waves to light and X- or -rays. A Glimpse to the Future… Maxwell’s Equations Coulomb’s Law but reconfigured by Gauss, early 1800’s Gauss’s Law Carl, early 1800’s Faraday’s Law Michael, mid 1800 Ampere’s Law, with Maxwell’s addition Andre’-Marie, early 1800’s Where E is electric field, B is magnetic field; is flux – refers to the amount of something passing thru an area; 0 is permeability of free space; 0 is permittivity of free space; Note: 00 = (c2)-1 All 3 “fundamental constants”… see front of text. A Glimpse to the Future… Maxwell’s Equations The equations have many “standard” forms… and even… Where is called the Del operator and refers to a gradient or a change in space