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PHY 124: Introduction to Physics II Electricity and Magnetism Electric Forces and Fields Kartik Ghosh Why Electricity, Magnetism, Optics, and Modern Physics? Understand the Nature The Universe Made of all particles that exist and the space where all events occur Matters Everything exists in the universe is made from tiny Atoms Everything exists in the universe is made from tiny Atoms Fish Protein Amino Acid Atom: A very basic unit of matter The Bohr Model of an Atom • Nucleus: Protons with positive charge + Neutrons with no Charge • Electrons: Move around the nucleus with negative charge • Number of electrons = Number of protons in an Atom. • Atom is always neutral The Bohr Model of Atom and Photon Bohr’s Postulates: Stationary States: Electrons in certain orbit without radiation Atom radiates only when electron makes a transition from one to other state Frequency of the photon is given by hf = Ei-Ef Everything is made using these Atoms only Elementary Particles Electron: Fundamental Subatomic Particle Mass (me) = 9.11x10-31 kg Charge (e) = -1.60 x 10-19 Coulomb or C Spin = 1/2 Proton and Neutron Proton: Fundamental Subatomic Particle Mass (mp) = 1.673x10-27 kg Charge (e) = 1.602 x 10-19 Coulomb or C Spin = 1/2 Neutron: Fundamental Subatomic Particle Mass (mn) = 1.675x10-27 kg Charge (e) = 0 Spin =1/2 Photon Charge = 0 Rest Mass = 0 Spin = 1 Speed of light in vacuum (c) = constant c = 2.99792458 x108 ~ 3 x 108 m/s Electricity, Magnetism, Optics, Modern Physics Electrostatics: Interaction among charges Electricity and Magnetism : Movement of the charge particles Optics and Modern Physics: Interaction among electrons or atoms with photons Two Important Elementary Particles Electron Photon Electrostatics (Ch-20 &Ch-21) Electric Charges and Forces Charges, Atoms, and Molecules Coulomb’s Law (Force between Charges) The Concept of the Electric Field Applications of the Electric Field Conductors in Electric Fields Forces and Torques on Charges in Electric Fields Electric Potential Energy and the Electric Potential Using the Electric Potential Calculating the Electrical Potential Sources of Electric Potential Connecting Potential and Field The Electrocardiogram Capacitance and Capacitors Dielectrics and Capacitors Energy and Capacitors What Will We Learn From Electrostatics? Total charge in any system: Q Electric Field at any point: E Electric Potential at any point: V Force between charges: F Energy in any system: U Chapter 20: Electric Charges, Forces and Fields • Electric Charges and Forces • Charges, Atoms, and Molecules • Coulomb’s Law (Force between Charges) • The Concept of the Electric Field • Applications of the Electric Field • Conductors in Electric Fields • Forces and Torques on Charges in Electric Fields Electric Charge Electron: Fundamental Subatomic Particle Mass (me) = 9.11x10-31 kg Charge (e) = -1.60 x 10-19 Coulomb or C Spin = 1/2 Discovering Electricity-I Expt-1 Nothing Happens Expt-2 Repel each other Expt-3 Attract each other Discovering Electricity-II Expt-4 Expt-5 Two Charged Rods Greater forces with more rubbing Less forces with increasing distance Weakly attracted with wool Weakly repelled with Silk Expt-6 Both rods attract the paper Charge Model I 1. Charging: Transfer of charge by rubbing or some other way 2. Two kinds of charge: Positive and negative 3. Like charges repel and opposite charges attract 4. Magnitude of force increases with the increase of charges and decreases with the increase of separation 5. Neutral objects have an equal number of positive and negative charges Discovering Electricity-III Expt-7 Same charge as plastic Expt-8 Same charge as plastic One has charge and other does not Expt-9 Same charge as plastic Both have charges Visualization of Charge Charge Model II 6. Two types of materials. Conductors and Insulators In conductors charges move easily and in Insulators charges are remain fixed in place 7. Charges can be transferred from one object to another by contact 8. Total charge in the universe is conserved: it can not be created or destroyed by any physical process Visualization of charges 6. Two types of materials. Conductors and Insulators In conductors charges move easily and in Insulators charges are remain fixed in place 7. Charges can be transferred from one object to another by contact 8. Total charge in the universe is conserved: it can not be created or destroyed by any physical process Triboelectric Charging Material Rabbit fur Glass Human hair Nylon Silk Relative charging with rubbing ++++++ +++++ ++++ +++ ++ Paper Cotton Wood Amber + ---- Rubber PVC Teflon ------------- Electroscope Charge Polarization Charging by Induction (Polarization) Polarization Polarization induces opposite charges on the surface Charging by Induction (Polarization) Polarization: Applications Pulling water Attracting neutral object Quantization of Charges Charge is quantized, occurring in “bits” of e, the magnitude of the fundamental charge on the electron or proton Charges, Atoms, and Molecules Model View of an Atom Atomic view of charging Electric Dipoles Hydrogen Bonding Hydrogen Bonds in DNA Forces between Charges ( Coulomb’s Law) Coulomb’s Law F q1 F q2 1 F 2 r Fk q1 q 2 r2 k 8.99 109 N.m2 /C 2 k 9.0 109 N.m2 /C 2 F12 F21 Comparison of Gravitational and Electrical Forces Forces between electron and proton in an atom Gravitational Force m1m 2 r2 (6.671011 N.m2 /kg2 )(9.111031 kg)(1.6731027 kg) (5.291011 m)2 Fg G 47 3.6310 N ElectricalForce Fe k q1 q 2 r2 (8.99109 N.m2 /C 2 )(1.6 1019 C )(1.6 1019 C ) (5.291011 m) 2 8.22108 N Elect ricalForce Fe 39 2.26 10 Fg Fe 2.26 1039 Fg Fe Fg Forces on a charge due to other charges Fnet F1onj F2onj F3onj ..... Fnet Fj1 Fj2 Fj3 ..... Fnet F12 F13 F14 Examples Forces in One Dimension If q1 = q2 , Then Fnet=0 Forces in One Dimension Where do they collide? (a) Close to A (b) Close to B (c) At C Location of a Zero net Force x F31 F32 k q1 q 3 x 2 k q 2 q3 (1- x)2 Forces in Two Dimension Forces in Two Dimension Superposition of Forces Determine a net force on a particular charge by all other charges 1. Find t hedirect ionof t heforces: F31F32 , ... 2. Find magnit udeof t heforces: F31 , F32 , .. 3. Choose your convenientx - and y - axes 4. Calculat ecomponent of s all forces 5. (a) Add all x - componet s- - - Gives result antX - comp- - Fx (b) Add all y - component -s - - Gives result antY - comp- - Fy 6. Get t hemagnit udeof t he t ot alforceusing t hefollowingformula Ftot Fx2 Fy2 7. Get t hedirect ionof t he t ot alforce: Fy θ t an Fx -1 How does the net force compare? The net force at A is (a) Less than at B (b) Greater than at B (c) Equal to at B -q charge is placed at either point A or B How does the net force compare? Uniform Spherical Charge Distributions Can be treated as total charge of the sphere located at the center of the sphere The velocity of an electron in Bohr Orbits CoulombForce: Fe k q1 q 2 r2 r Bohr radius me v2 Cent ripet al Force r Cent ripet al Force CoulombForce q1 q 2 me v2 k 2 r r k ve mer Velocity of an electron v = ? For the first orbit v = 2.19 x 106 m v 1 r The Concept of an Electric Field Presence of Charge alters the space around it be creating an electric field. The Electric Field of a Point Charge Electric Field ElectricFlux E : Force per chargeat a given location F E , q' is a positivetest charge q' ElectricField due to a chargeq is E kq r2 Superposition of Fields Same as Force: Vector sum of the fields due to all charges Electric Field Lines Rules for Drawing Electric Field Lines ElectricField Lines 1. P ointin thedirectionof theelectricfield vectorat everypoint 2.Start at ve chargesor at Infinity 3. Ends at - ve chargesor at Infinity 4. Are moredense where electricfield has greatermagnit ude Electric Field Lines for a Point Charge Electric Field Lines for Systems of Charges Electric Field Lines for Systems of Charges Which is true? Electric Field Lines for Systems of Charges Electric Field Lines in A Parallel-Plate Capacitor What are the signs of q1 and q2? Conductors in Electric Fields Any excess charge placed on a conductor moves to its exterior surface At equilibrium E = 0 within a conductor A conductor shield a cavity within it from external electric fields Ground is a good conductor Grounding: Connect a conductor to the ground Conductors in Electric Fields Conductors in Electric Fields Forces on Charges in Electric Fields F qE Forces and Torques on a dipole in Electric Fields F qE F qE qEL Problems Charges A container holds a gas consisting of 1.50 moles of oxygen molecules. One in a million of these molecules has lost a single electron. What is the net charge of the gas? 1 mole of gas has N = 6.022 x 1023 molecules 1 (1.50 mol)(6.022 1023 mol1 ) 106 19 C) 0.145 C (1.60 10 Problems Force Find the direction and magnitude of the net electrostatic force exerted on the point charge q2. Let q=+2.4 mC and d =33 cm Problems Determine a net force on a particular charge by all other charges 1. Find thedirectionof theforces: F21F23 , ... 2. Find magnitudeof theforces: F21 , F23 , .. F21 F1 , F23 F3 , F24 F4 3. Choose your convenientx - and y - axes 4. Calculatecomponentsof all forces 5. (a) Add all x - componets- - - Gives resultantX - comp- - Fx (b) Add all y - components- - - Gives resultantY - comp- - Fy 6. Get themagnitudeof the totalforceusing thefollowingformula Ftot Fx2 Fy2 7. Get thedirectionof the totalforce: Fy θ tan-1 Fx F Fx xˆ Fy yˆ Problems Let q2 be at the origin and q3 be on the positive x-axis. F1 F3 kq1q2 2 d kq2 q3 2 yˆ xˆ kq(2.0q) 2 yˆ d k (2.0q)(3.0q ) 2 2.0kq 2 d 2 xˆ yˆ 6.0kq 2 2 xˆ d d d kq2 q4 xˆ yˆ k (2.0q)(4.0q) xˆ yˆ 2.0 2kq 2 F4 ( xˆ yˆ ) 2 2 2 2 2 ( 2d ) 2 2d 2 d 2.0 2kq 2 6.0kq 2 2.0 2kq 2 2.0kq 2 2.0kq 2 Fnet [( 2 3.0)xˆ ( 2 1)yˆ ] xˆ yˆ 2 2 2 2 2 d d d d d Fnet 2 2.0 8.99 109 Nm2 (2.4 10 6 C)2 tan 1 C (0.33m)2 2 1 2 3.0 ( 2 3.0) 2 ( 2 1) 2 4.2 N 5.4 180 174.6 Problems Electric Fields Consider a system consisting of three charges, q1 =+5.00 mC, q2= +5.00 mC and q3 = -5.00 mC, at the vertices of an equilateral triangle of side d = 2.75 cm (a) Find the magnitude of the electric field at a point halfway between the charges q1 and q2 (b) Is the magnitude of the electric field halfway between the charges q2 and q3 greater than, or less than, or the same as the electric field found in part (a)? Explain. (c) Find the magnitude of the electric field at the point specified in part (b). Problems Let q1 be at the origin and q3 be on the positive x-axis. At a point halfway between charges q1 and q2 the contributions to the electric field attributed to each of those charges cancel one another. The remaining contribution comes from q3 2 9 Nm 6 8.99 10 (5.00 10 C) 2 C kq E 3 7.93 107 N/C 2 2 r2 0.0275 m (0.0275 m) 2 Problems At this location, the electric fields of q2and q3 add, and the resulting field points toward q3. The field due to q1 will have the same magnitude as found in part (a), and will be perpendicular to the combined fields of q2 and q3. The vector sum of the electric fields from all three charges will have a magnitude greater than that found in part (a k q1 2 3 2 E1 (cos 30xˆ sin 30yˆ ) xˆ yˆ 2 2 3 d 3 d 2 d2 k q1 E2 k q2 E3 k q3 d 2 2 d 2 2 (cos 60xˆ sin 60yˆ ) k q2 d (cos 60xˆ sin 60yˆ ) 2 k q3 d 2 2xˆ 2 3yˆ 2xˆ 2 3yˆ Problems Enet E1 E2 E3 kq 2 3 2 Enet 4 xˆ 4 3 yˆ 2 3 3 d 2 Enet 2 kq 2 3 2 4 4 3 2 3 3 d (8.99 109 N m 2 / C )(5.00 106 C)(8.110) (2.75 102 m) 2 4.82 108 N/C The End