Buoyancy and Archimedes Principle

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1 Buoyancy and Archimedes Principle This is an object submerged in a fluid. There is a net force on the object because the pressures at the top and bottom of it are different. The buoyant force is found to be the upward force on the same volume of water: P=ρgh and F=PA and m=ρv 2016 Pearson Education, Ltd. 1

2 Estimation of the absolute coefficient of liquid viscosity with the Stokes method

3 Estimation of the absolute coefficient of liquid viscosity with the method of falling balls is based on the Stokes law indicating the resistance (F) encountered by a ball falling in the liquid with the uniform motion and velocity (v) (1) F = 6 v r where: η liquid viscosity coefficient r ball radius [m] v ball velocity [m/s]

4 The ball s falling proceeds with uniform motion from the moment of balancing the gravity force (P) with the resistance force (F) and the hydrostatic lift of the liquid (W). (2) The weight P = F +W of the ball may be expressed as: (3) P =m 1 xg= 4/3 π r 3 d 1 g and the hydrostatic lift as: (4) W = m 2 xg=4/3 π r 3 d 2 g where: d1 - density of the ball [kg/m3] d2 - density of the liquid (d2 = 1230 (1) F = 6 r n kg/m3) substituting the expression (1), (3), (4) to the equation (2) we g -acceleration of gravity (g = 9,81 N/kg) obtain:

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9 ELECTRIC CHARGE AND ELECTRIC FIELD D R M A R T A S T A S I A K D E P A R T M E N T O F C Y T O B I O L O G Y A N D P R O T E O M I C S lecture based on 2016 Pearson Education, Ltd.

10 CONTENTS Static Electricity; Electric Charge and Its Conservation Electric Charge in the Atom Insulators and Conductors Induced Charge; the Electroscope Coulomb s Law Solving Problems Involving Coulomb s Law and Vectors The Electric Field Electric Field Lines Electric Fields and Conductors Electric Forces in Molecular Biology: DNA Structure and Replication Photocopy Machines and Computer Printers Use Electrostatics

11 STATIC ELECTRICITY; ELECTRIC CHARGE AND ITS CONSERVATION Objects can be charged by rubbing

12 STATIC ELECTRICITY; ELECTRIC CHARGE AND ITS CONSERVATION Charge comes in two types, positive and negative; like charges repel opposite charges attract

13 STATIC ELECTRICITY; ELECTRIC CHARGE AND ITS CONSERVATION Central rule of electricity: Opposite charges attract one another; like charges repel.

14 STATIC ELECTRICITY; ELECTRIC CHARGE AND ITS CONSERVATION Electric charge is conserved the arithmetic sum of the total charge cannot change in any interaction.

15 ELECTRIC CHARGE IN THE ATOM Atom: Nucleus (small, massive, positive charge) Electron cloud (large, very low density, negative charge)

16 ELECTRIC CHARGE IN THE ATOM Atom is electrically neutral. Rubbing charges objects by moving electrons from one to the other.

17 ELECTRIC CHARGE IN THE ATOM Polar molecule: neutral overall, but charge not evenly distributed

18 CHARGE BALANCE Neutral atoms are made of equal quantities of positive and negative charges Neutral carbon has 6 protons, 6 electrons, (& neutrons) Electrons can be stripped off of atoms Electrons occupy the vulnerable outskirts of atoms Usually charge flows in such a way as to maintain neutrality Excess positive charge attracts excess negative charge Your body has positive charges and negative charges, balanced within millions or billions

19 CHARGE SEPARATION Can separate charges by rubbing: feet on carpet atmosphere across ground silk on glass balloon on hair!

20 INSULATORS AND CONDUCTORS Conductor: Insulator: Charge flows freely Almost no charge flows Metals Most other materials Some materials are semiconductors. Conductor: Insulator:

21 INDUCED CHARGE; THE ELECTROSCOPE Metal objects can be charged by conduction:

22 INDUCED CHARGE; THE ELECTROSCOPE Nonconductors won t become charged by conduction or induction, but will experience charge separation:

23 INDUCED CHARGE; THE ELECTROSCOPE The electroscope can be used for detecting charge:

24 INDUCED CHARGE; THE ELECTROSCOPE The electroscope can be charged either by induction or by conduction.

25 INDUCED CHARGE; THE ELECTROSCOPE The charged electroscope can then be used to determine the sign of an unknown charge.

26 COULOMB S LAW Experiment shows that the electric force between two charges is proportional to the product of the charges and inversely proportional to the distance between them.

27 Coulomb s law: COULOMB S LAW ELECTROSTATIC FORCE This equation gives the magnitude of the force. Unit of charge: coulomb, C The proportionality constant in Coulomb s law is then: k = N m 2 /C 2 Charges produced by rubbing are typically around a microcoulomb: 1 µc = 10 6 C Looks a lot like Newton s gravitation in form Electron and proton attract each other times stronger electrically than gravitationally! Good thing charge is usually balanced!

28 COULOMB S LAW Charge on the electron: e = C Electric charge is quantized in units of the electron charge. The proportionality constant k can also be written in terms of ε 0, the permittivity of free space:

29 COULOMB LAW ILLUSTRATED + + r + If charges are of same magnitude (and same separation), all the forces will be the same magnitude, with different directions.

30 COULOMB S LAW Coulomb s law strictly applies only to point charges. Superposition: for multiple point charges, the forces on each charge from every other charge can be calculated and then added as vectors.

31 SOLVING PROBLEMS INVOLVING COULOMB S LAW AND VECTORS The net force on a charge is the vector sum of all the forces acting on it.

32 THREE CHARGES IN A LINE

33 SOLVING PROBLEMS INVOLVING COULOMB S LAW AND VECTORS Vector addition review:

34 THE ELECTRIC FIELD The electric field is the force on a small charge, divided by the charge:

35 THE ELECTRIC FIELD For a point charge:

36 THE ELECTRIC FIELD Force on a point charge in an electric field: Superposition principle for electric fields:

37 THE ELECTRIC FIELD Problem solving in electrostatics: electric forces and electric fields 1. Draw a diagram; show all charges, with signs, and electric fields and forces with directions 2. Calculate forces using Coulomb s law 3. Add forces vectorially to get result

38 ELECTRIC FIELD LINES The electric field can be represented by field lines. These lines start on a positive charge and end on a negative charge.

39 ELECTRIC FIELD LINES The number of field lines starting (ending) on a positive (negative) charge is proportional to the magnitude of the charge. The electric field is stronger where the field lines are closer together.

40 ELECTRIC FIELD LINES Electric dipole: two equal charges, opposite in sign:

41 ELECTRIC FIELD LINES The electric field between two closely spaced, oppositely charged parallel plates is constant.

42 ELECTRIC FIELD LINES Summary of field lines: 1. Field lines indicate the direction of the field; the field is tangent to the line. 2. The magnitude of the field is proportional to the density of the lines. 3. Field lines start on positive charges and end on negative charges; the number is proportional to the magnitude of the charge.

43 ELECTRIC FIELDS AND CONDUCTORS The static electric field inside a conductor is zero if it were not, the charges would move. The net charge on a conductor is on its surface.

44 ELECTRIC FIELDS AND CONDUCTORS The electric field is perpendicular to the surface of a conductor again, if it were not, charges would move.

45 ELECTRIC FORCES IN MOLECULAR BIOLOGY: DNA STRUCTURE AND REPLICATION Molecular biology is the study of the structure and functioning of the living cell at the molecular level. The DNA molecule is a double helix:

46 ELECTRIC FORCES IN MOLECULAR BIOLOGY: DNA STRUCTURE AND REPLICATION The A-T and G-C nucleotide bases attract each other through electrostatic forces.

47 ELECTRIC FORCES IN MOLECULAR BIOLOGY: DNA STRUCTURE AND REPLICATION Replication: DNA is in a soup of A, C, G, and T in the cell. During random collisions, A and T will be attracted to each other, as will G and C; other combinations will not.

48 PHOTOCOPY MACHINES AND COMPUTER PRINTERS USE ELECTROSTATICS 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

49 PHOTOCOPY MACHINES AND COMPUTER PRINTERS USE ELECTROSTATICS

50 PHOTOCOPY MACHINES AND COMPUTER PRINTERS USE ELECTROSTATICS Laser printer is similar, except a computer controls the laser intensity to form the image on the drum

51 SUMMARY Two kinds of electric charge positive and negative Charge is conserved Charge on electron: e = C Conductors: electrons free to move Insulators: nonconductors Charge is quantized in units of e Objects can be charged by conduction or induction Coulomb s law: Electric field is force per unit charge:

52 SUMMARY Electric field of a point charge: Electric field can be represented by electric field lines Static electric field inside conductor is zero; surface field is perpendicular to surface

53 ELECTRIC CHARGE Recall that fundamental particles carry something called electric charge: protons have exactly one unit of positive charge electrons have exactly one unit of negative charge Electromagnetic force is one of the basic interactions in nature like charges experience repulsive force opposite charges attracted to each other (like gravity) Electrical current is flow of charge (electrons)

54 STATIC ELECTRICITY Rubbing action redistributes charge (unbalanced) If enough charge builds up, we get discharge Air spark is actually due to breakdown of air neutral air molecules separate into ions (electrons are stripped away) current can then flow through the plasma-field air In essence, air becomes a wire for a short bit this happens at 3 million volts per meter 1 cm spark then at 30,000 volts typical finger-spark may involve a few billion electrons hold onto key to reduce pain of spark

55 LIGHTNING Lightning is an unbelievably huge discharge Clouds get charged through air friction 1 kilometer strike means 3 billion volts! (1cm V) Main path forms temporary wire along which charge equalizes often bounces a few times before equal Thunder is bang produced by the extreme pressure variations induced by the formation and collapse of the plasma conduit html

56 LIGHTNING RODS Perform two functions provide safe conduit for lightning away from house diffuse situation via coronal discharge Charges are attracted to tip of rod, and electric field is highly concentrated there. Charges leak away, diffusing charge in what is sometimes called St. Elmo s Fire, or coronal discharge

57 ELECTRIC FIELDS IN CIRCUITS Point away from positive terminal, towards negative Channeled by conductor (wire) Electrons flow opposite field lines (neg. charge) E electrons & direction of motion E E Electric field direction E

58 ELECTRON BEAMS; CATHODE RAY TUBES (CRTS) Televisions, Oscilloscopes, Monitors, etc. use an electron beam steered by electric fields to light up the (phosphorescent) screen at specified points screen cathode emitter electron beam E-field metal plates

59 ELECTRIC POTENTIAL

60 ELECTRIC POTENTIAL Electric potential energy Energy possessed by a charged particle due to its location in an electric field. Work is required to push a charged particle against the electric field of a charged body.

61 ELECTRIC POTENTIAL (a) The spring has more mechanical PE when compressed. (b) The charged particle similarly has more electric PE when pushed closer to the charged sphere. In both cases, the increased PE is the result of work input.

62 ELECTRIC POTENTIAL Electric potential (voltage) Energy per charge possessed by a charged particle due to its location May be called voltage potential energy per charge In equation form: Electric potential = electric potential energy amount of charge

63 ELECTRIC POTENTIAL Electric potential (voltage) (continued) Unit of measurement: volt, 1 volt = Example: 1 joule 1 coulomb Twice the charge in same location has twice the electric potential energy but the same electric potential. 3 times the charge in same location has 3 times the electric potential energy but the same electric potential (2 E/2 q = 3 E/3 q = V )

64 ELECTRIC POTENTIAL Electric potential (voltage) (continued) High voltage can occur at low electric potential energy for a small amount of charge. High voltage at high electric potential energy occurs for lots of charge.

65 ELECTRIC POTENTIAL CHECK YOUR NEIGHBOR Electric potential energy is measured in joules. Electric potential, on the other hand (electric potential energy per charge), is measured A. in volts. B. in watts. C. in amperes. D. also in joules.

66 ELECTRIC POTENTIAL CHECK YOUR ANSWER Electric potential energy is measured in joules. Electric potential, on the other hand (electric potential energy per charge), is measured A. in volts. B. in watts. C. in amperes. D. also in joules.

67 EQUIPOTENTIAL LINES AND SURFACES An equipotential is a line or surface over which the potential is constant. Electric field lines are perpendicular to equipotentials. The surface of a conductor is an equipotential.

68 EQUIPOTENTIAL LINES AND SURFACES Equipotential lines of an electric dipole:

69 THE ELECTRON VOLT, A UNIT OF ENERGY One electron volt (ev) is the energy gained by an electron moving through a potential difference of one volt.

70 ELECTRIC POTENTIAL DUE TO POINT CHARGES The electric potential due to a point charge can be derived using calculus. The potential due to an electric dipole is just the sum of the potentials due to each charge, and can be calculated exactly.

71 CAPACITANCE A capacitor consists of two conductors that are close but not touching. A capacitor has the ability to store electric charge.

72 CAPACITANCE (a) Parallel-plate capacitor connected to battery. (b) is a circuit diagram..

73 CAPACITANCE When a capacitor is connected to a battery, the charge on its plates is proportional to the voltage: The quantity C is called the capacitance. Unit of capacitance: the farad (F) 1 F = 1 C/V The capacitance does not depend on the voltage; it is a function of the geometry and materials of the capacitor. For a parallel-plate capacitor:

74 DIELECTRICS A dielectric is an insulator, and is characterized by a dielectric constant K. Capacitance of a parallel-plate capacitor filled with dielectric:

75 DIELECTRICS Dielectric strength is the maximum field a dielectric can experience without breaking down

76 DIELECTRICS The molecules in a dielectric tend to become oriented in a way that reduces the external field.

77 DIELECTRICS This means that the electric field within the dielectric is less than it would be in air, allowing more charge to be stored for the same potential.

78 STORAGE OF ELECTRIC ENERGY A charged capacitor stores electric energy; the energy stored is equal to the work done to charge the capacitor. The sudden discharge of electric energy can be harmful or fatal. Capacitors can retain their charge indefinitely even when disconnected from a voltage source be careful!

79 STORAGE OF ELECTRIC ENERGY Heart defibrillators Is a capacitor charged to a high voltage ( a few thousand volts) use electric discharge very rapidly trough the heart via a pair of wide contacts known as paddles to jump-start the heart when its beats become irregular (ventricular or cardiac fibrillation), and can save lives.

80 DIGITAL; BINARY NUMBERS; SIGNAL VOLTAGE Analog signal voltages vary continuously.

81 DIGITAL; BINARY NUMBERS; SIGNAL VOLTAGE Digital signals use binary numbers to represent numerical values.

82 DIGITAL; BINARY NUMBERS; SIGNAL VOLTAGE In order to convert an analog signal to digital, the signal must be sampled. A higher sampling rate reproduces the signal more precisely.

83 DIGITAL; BINARY NUMBERS; SIGNAL VOLTAGE Before it is sent to a loudspeaker or headset, a digital audio signal must be converted back to analog. Noise can easily corrupt an analog signal; a digital signal is much less sensitive to noise.

84 ELECTROCARDIOGRAM (ECG OR EKG) The electrocardiogram detects heart defects by measuring changes in potential on the surface of the heart. Heart muscle cell showing (a)charge dipole layer in resting state (b) Depolarization processing as muscle begins to contract (c) Potential V at points P and P as a function of time

85 ELECTROCARDIOGRAM (ECG OR EKG) The typical electrocardiogram ECG Two heart beats are shown Divide into the regions corresponding to the various deflection (or waves), activity of particular part of the heart beat.

86 ELECTROCARDIOGRAM (ECG OR EKG) P- contraction of the arteria QRS- contraction of ventricles as the depolarization a very complicated path T- recovery (repolarization) S- becomes very large (negatively) if right side of heart is enlarges if the right ventricle must push against an abnormally large load Infarcts, witch are dead regions of the heart muscles that result from heart attracts, are also detected on an ECG because they reflect the depolarization wave

87 SUMMARY Electric potential is potential energy per unit charge: Electric potential difference: work done to move charge from one point to another Relationship between potential difference and field: Equipotential: line or surface along which potential is the same Electric potential of a point charge:

88 SUMMARY Electric dipole potential drops off as 1/r2 Capacitor: nontouching conductors carrying equal and opposite charge Capacitance: Capacitance of a parallel-plate capacitor: A dielectric is an insulator Dielectric constant gives ratio of total field to external field Energy density in electric field: Digital electronics convert analog signal to digital approximation using binary numbers

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