Electric Potential Energy & Voltage. Tesla Envy =jlzeqz4efqa&feature=related

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1 Electric Potential Energy & Voltage Tesla Envy =jlzeqz4efqa&feature=related

2 Ch 23 & 24: Electric Force and Field F qq k r 1 2rˆ 12 2 F qe kq Electric Field E due to q : E 1 1 r 2

3 Ch 25: ENERGY & VOLTAGE E is the FORCE FIELD: VECTOR V is the ENERGY FIELD: SCALAR The force field lines are everywhere perpendicular to the potential energy field lines

4 Gravitational Force Field and Potential Energy & Potential

5 Review: Work A force moving a mass through a displacement does WORK. If F is constant then W Fr Fr cos If F varies with r then along any radial segment dw Fdr F() r dr The total work is W r r i f F( r) dr

6 Review: Conservative Forces and Potential Energy A conservative force is defined as a vector field that is equal to the negative of the gradient of a scaler field the Poetential Energy function U: F x du dx The gradient of a scalar field at a point is a vector pointing in the direction of the steepest slope or grade at that point. The steepness of the slope at that point is THE FORCE!!! Leads to Work Energy Theorem and Conservation of Energy: x W F dx U K f x i x U K 0 E K U

7 Electric Potential Energy Since the Force is Conservative, the Work is independent of path. The work done by F along any radial segment is dw F( r) ds q E( r) ds The work done by a force that is perpendicular to the displacement is 0. ds = dr 0 The total work is B E 0 () A W q r d r Recall that the work done by a conservative force on an object is: W U K (As a rock falls, it loses PE but gains KE!!!)

8 Potential Difference in a Uniform Field B B B A E s s A A V V V d E d Ed Electric field lines always point in the direction of decreasing electric potential When the electric field is directed downward, point B is at a lower potential than point A When a positive test charge moves from A to B, the charge-field system loses potential energy

9 The Electric Field does work on the charge to move it a distance d from A to B, converting Potential Energy into Kinetic Energy, same as with the gravitational field. Conservation of Energy and the Work-Energy Theorem apply: U K W Fr r d U U E g qed mgh (Uniform Field Only)

10 Electric Potential The Electric Potential Energy per unit charge between A and B is called the Electric Potential Difference between A and B. For a uniform field: V V V B A U / q0 q Ed / q V Ed VAB 0 0 Ed Ed

11 Electric Potential High Potential V V V Es B A Unit for Electric Potential is the VOLT: 1 V = J/C = N m /C Electric Potential is a SCALAR! Only DIFFERENCES in potential between two points can be measured. There is no potential for a single point unless the other point is zero the ground. Electric Potential is NOT Potential Energy! + charges move from hi to low potential (think gravity water fall) - charges move from low to hi potential (think antigravity water pump) Low Potential

12 Potential Difference: VOLTAGE As a + particle moves from A to B, its electric potential energy changes by B A B E 0 () A U U U W q r dr Define the potential difference between points A and B V U / q V V V E ds B A 0 B A The electric potential is independent of the path It is customary to choose a reference potential of V = 0 at r A = E and V are perpendicular!!!

13 First: The Simplest Case Constant Force -Uniform Electric Fields V V V Es B A

14 Electron Volts What is the kinetic energy gained by an electron when it moves across a potential difference of 1 volt? Low Potential High Potential K U Vq 19 ( 1 V )( 1.6x10 C) 19 1 J / C(1.6 x10 C) 1.6x10 19 J ev x J Note: 5eV electron breaks organic bonds in molecules. Nuclear decay energies ~ 1MeV

15 Example What is the final speed of a free electron accelerated from rest through a potential difference of 1V? 1 K v U 2 2 mv qv 2qV m 19 2( 1.6x10 C)1V 5 v 5.93x10 m / s x10 kg

16 Potential High Potential Worksheet V V V Es B A Low Potential

17 Potential Difference: Signs

18 Example A 12V motorcycle battery moves 5000C of charge. How much energy does it deliver to that charge? U Vq 0 V U / q 0 12 V(5000 C) 12 J / C(5000 C) V 12V x10 J Potential (Voltage) is NOT Energy!

19 Problem What is the magnitude of the maximum voltage that can be sustained between 2 parallel plates separated by 2.5 cm of dry air? Dry air supports max field strength (dielectric strength CH 26) of 3x 10 6 V/m. V Es V V V Es B A (3x10 6 V)(.025 m) 7.5x10 4 V 75kV More than this and the air breaks down and becomes a conductor. LIGHTENING!

20 The dielectric breakdown strength of dry air, at Standard Temperature and Pressure (STP), between spherical electrodes is approximately 33 kv/cm.

21 Jacob s Ladder WARNING! Exposure to an arc-producing device can pose health hazards. In a closed space such as a classroom or home, the continuous arc formation of an open-air Jacob's Ladder will ionize oxygen and nitrogen, which then reforms into reactive molecules such as ozone and nitric oxide. These free radicals can be damaging to the mucous membranes of people near the spark gap. Time exposure

22 Sources of Electric Potential: Batteries 1.5 Volt Battery is the Voltage across the terminals. B A

23 Case 2: Potential Due to Point Charges & Varying Force

24 Potential and Point Charges A positive point charge produces a field directed radially outward The potential difference between points A and B will be B B B kq 1 1 VB VA V E ds E dr dr kq A A A 2 r rb ra 1 1 VB VA keq r B r A The electric potential is independent of the path between points A and B It is customary to choose a reference potential of V = 0 at r A = Then the potential at some point r is: V q ke r

25 PROBLEM What is the electric potential 1.2m from a point charge Q = + 4x10-8 C. How does the potential change if the charge is positive or negative? Q Point Charge: V ( r) k r V ( r) 9.00x Nm 4x10 C C Vr ( ) 300 Nm C 2 1.2m r V( r) 300V (Note: If Q is negative, V is negative!)

26 V The Electric Field is the Negative of the Slope (Gradient) of the Electric Potential! q dv q ke Er E ke 2 r dr r The gradient of a scalar field at a point is a vector pointing in the direction of the steepest slope or grade at that point. The steepness of the slope at that point is given by the magnitude of the gradient vector.

27 V V V Es B A E V s

28 V V V E ds B A B A E V s

29 E V s

30 E V s

31 In Sum: Potential due to a Point Charge The potential a distance r from a point charge is given by: V () r Q k r V is the potential difference between r and infinity where the potential is taken to be zero (the ground is at infinity.) V gives the amount of energy per unit charge that it takes to bring a test charge from infinity to r. r The total potential due to a distribution of charge is equal to the algebraic sum of all the potentials (not vector sum!) The sign of the charge matters!!!

32 Multiple Charges The electric potential due to several point charges is the sum of the potentials due to each individual charge, taking the potential at infinity equal to zero and r is the distance from the charge to the point P: V k q i i ri The potential energy of the system is U q 0 V U qq k r

33 Problem Determine the electric potential at point A & B due to a dipole A proton is placed at point A and released. What is the change in potential energy of the proton between A and B? What is the velocity of the proton at B?

34 Electric Potential of a Dipole

35 U for System of Static Charges The potential energy of a system of charges is the energy needed to assemble them from infinity where U = 0. The total U includes a term for every pair of charges!!! For two charges it is: qq 1 2 U k r 12 For three charges: U net qq k i j r ij ij U qq 1 2 q q q q k r12 r13 r

36 Potential Energy Problem Determine the electric potential energy of the triangular group. That is, find the work done to bring them from infinity to the triangular arrangement. Is there a place interior to the group where the potential is zero? The side of the triangle is 0.50m. V k q i i ri U qq q q q q ke r12 r13 r23 U net qq k i j r ij ij

37 Sample Problem Old Exam Problem

38 Case 4: Electric Potential for ANY Continuous Charge Distribution In general, the potential at some point due to a small charge element dq is dq dvp ke r dq VP ke V( )=0 r

39 Nonuniform Continuous Charge Distribution, total charge Q x 0 dq VP ke V( )=0 r

40 As shown in the text V for a Uniformly Charged Ring Easier to calculate V because it is a scalar! Find E from the gradient. V k dq kq r a x 2 2 E x dv dx E( x) kxq 2 2 x a 3/2 iˆ

41 V for a Uniformly Charged Disk The ring has a radius R and surface charge density of σ P is along the perpendicular central axis of the disk E x dv dx V 2πkσ R x x E Disk 2k 1 x x R 2 2

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43 Cavity in a Conductor Assume an irregularly shaped cavity is inside a conductor Assume no charges are inside the cavity The electric field inside the conductor must be zero

44 Cavity in a Conductor, cont The electric field inside does not depend on the charge distribution on the outside surface of the conductor For all paths between A and B, V B V d A E s B A A cavity surrounded by conducting walls is a field-free region as long as no charges are inside the cavity 0

45 V Due to a Charged Conductor The potential difference between A and B is also zero The charge density is high where the radius of curvature is small And low where the radius of curvature is large The electric field is large near the convex points having small radii of curvature and reaches very high values at sharp points

46 Corona Discharge If the electric field near a conductor is sufficiently strong, electrons resulting from random ionizations of air molecules near the conductor accelerate away from their parent molecules These electrons can ionize additional molecules near the conductor This creates more free electrons The corona discharge is the glow that results from the recombination of these free electrons with the ionized air molecules The ionization and corona discharge are most likely to occur near very sharp points Low energy corona discharge surrounding a circular conductor.

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49 Corona Discharge Corona Discharge Supersonic Free-Jet (CDSFJ) to generate excited-state molecular nitrogen for growing III-N semiconductors..

50 Corona Discharge Corona discharge into free air

51 Jacob s Ladder WARNING! Exposure to an arc-producing device can pose health hazards. In a closed space such as a classroom or home, the continuous arc formation of an open-air Jacob's Ladder will ionize oxygen and nitrogen, which then reforms into reactive molecules such as ozone and nitric oxide. These free radicals can be damaging to the mucous membranes of people near the spark gap. Time exposure

52 Van de Graaff Generator Charge is delivered continuously to a high-potential electrode by means of a moving belt of insulating material The high-voltage electrode is a hollow metal dome mounted on an insulated column Large potentials can be developed by repeated trips of the belt Protons accelerated through such large potentials receive enough energy to initiate nuclear reactions

53 Electrostatic Precipitator An application of electrical discharge in gases is the electrostatic precipitator It removes particulate matter from combustible gases The air to be cleaned enters the duct and moves near the wire As the electrons and negative ions created by the discharge are accelerated toward the outer wall by the electric field, the dirt particles become charged Most of the dirt particles are negatively charged and are drawn to the walls by the electric field

54 Application Xerographic Copiers The process of xerography is used for making photocopies Uses photoconductive materials A photoconductive material is a poor conductor of electricity in the dark but becomes a good electric conductor when exposed to light

55 The Xerographic Process

56 Application Laser Printer The steps for producing a document on a laser printer is similar to the steps in the xerographic process A computer-directed laser beam is used to illuminate the photoconductor instead of a lens

57 Millikan Oil-Drop Experiment Experimental Set-Up PLAY ACTIVE FIGURE

58 Millikan Oil-Drop Experiment Robert Millikan measured e, the magnitude of the elementary charge on the electron He also demonstrated the quantized nature of this charge Oil droplets pass through a small hole and are illuminated by a light

59 Oil-Drop Experiment, 2 With no electric field between the plates, the gravitational force and the drag force (viscous) act on the electron FThe D mdrop g reaches terminal velocity with

60 Oil-Drop Experiment, 3 When an electric field is set up between the plates The upper plate has a higher potential The drop reaches a new terminal velocity when the electrical force equals the sum of the drag force and gravity

61 Oil-Drop Experiment, final The drop can be raised and allowed to fall numerous times by turning the electric field on and off After many experiments, Millikan determined: q = ne where n = 0, -1, -2, -3, e = 1.60 x C This yields conclusive evidence that charge is quantized Use the active figure to conduct a version of the experiment

62 Case 3: Electric Potential Given the Electric Field If there is sufficient symmetry then you can use Gauss s Law to find the E field and find the potential difference from V V V Eds B A B A Choose V = 0 at some convenient point, usually infinity.

63 The electric potential is a function of r The electric field is a function of r 2 The effect of a charge on the space surrounding it: The charge sets up a vector electric field which is related to the force The charge sets up a scalar potential which is related to the energy E Compared to V

64 Bohr Orbital Binding Energy for Single Electron Atoms E n Z 13.6eV n 2 2 Ground State: n = 1 First Excited: n = 2 2 nd Excited: n = eV is the energy of the H ground state. 2. Negative because it is the Binding Energy and work must be done on the atom (by a photon) to ionize it. 3. A 13.6eV photon must be absorbed to ionize the ground state

65 Binding Energy in Molecules