Gravity and Electrostatics

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Gravity and Electrostatics • Newton’s Law of Gravity. Two masses, m1 and m2 , experience gravitational attractive force to each other, that depends on distance between them, r: Gm m m3 F = − 1 2 ; G = 6.710 −11 r 2 kg s 2 G is called Gravitational Constant. In this equation, ‘-’ sign stands for attraction (positive direction is “away”) . • Coulomb’s Law. Two electric charges, q1 and q2 , at distance r, act onto each other with electrostatic force given by Coulomb’s formula: kq q Nm2 Fk=12; =9 109 rC22 Here k is called Coulomb’s constant . SI unit of electric charge is 1 Coulomb (1C), which is a very large charge. Coulomb’s Law is very similar to Newton’s, but • Electric charges can be positive or negative, unlike masses. • Note that the signs in two laws are different. As a result, charges of the same sign repel, while the opposite ones attract each other. Electric Field • A Field is a physical quantity that has certain value at any point of physical space (x,y,z), and time, t. In other words, it’s a function defined in physical space & time. • Electric Field = electric force acting on a probe charge q, divided by q: F E = elect q • Once the electric field is known at certain point (x,y,z), one can find the electric force acting on any charge Q placed at that point: Felect = QE Homework Problem 1 a) By using Newton’s law of gravity, find the gravitational acceleration on the surface of a planet with mass M and radius R. For doing this, consider an apple of mass m. Its weight is mg. But it also must be equal to Newton’s gravitational force. b) Imagine that you discovered a planet with the same density as Earth, but its radius is twice as big. What will be the value of g on that planet? Problem 2 Find the magnitude of the electric field E at the point half way between two charges, q1 and q2 placed at distance d from each other..

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Coulomb's Force
COULOMB’S FORCE LAW Two point charges Multiple point charges Attractive Repulsive - - + + + The force exerted by one point charge on another acts along the line joining the charges. It varies inversely as the square of the distance separating the charges and is proportional to the product of the charges. The force is repulsive if the charges have the same sign and attractive if the charges have opposite signs. q1 Two point charges q1 and q2 q2 [F]-force; Newtons {N} [q]-charge; Coulomb {C} origin [r]-distance; meters {m} [ε]-permittivity; Farad/meter {F/m} Property of the medium COULOMB FORCE UNIT VECTOR Permittivity is a property of the medium. Also known as the dielectric constant. Permittivity of free space Coulomb’s constant Permittivity of a medium Relative permittivity For air FORCE IN MEDIUM SMALLER THAN FORCE IN VACUUM Insert oil drop Viewing microscope Eye Metal plates Millikan oil drop experiment Charging by contact Example (Question): A negative point charge of 1µC is situated in air at the origin of a rectangular coordinate system. A second negative point charge of 100µC is situated on the positive x axis at the distance of 500 mm from the origin. What is the force on the second charge? Example (Solution): A negative point charge of 1µC is situated in air at the origin of a rectangular coordinate system. A second negative point charge of 100µC is situated on the positive x axis at the distance of 500 mm from the origin. What is the force on the second charge? Y q1 = -1 µC origin X q2= -100 µC Example (Solution): Y q1 = -1 µC origin X q2= -100 µC END Multiple point charges It has been confirmed experimentally that when several charges are present, each exerts a force given by on every other charge.
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S.I. and Cgs Units
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Communications-Mathematics and Applied Mathematics/Download/8110
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Fundamental Physical Constants: Explained and Derived by Energy Wave Equations
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Hydrogen Atom – Lyman Series Rydberg’S Formula Hydrogen 91.19Nm Energy Λ = Levels 1 1 0Ev − M2 N2
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Where Do We See Electricity and Magnetism? a Brief Walk Through History
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Coulomb Balance
Includes 012-03760E Teacher's Notes Instruction Manual and and 05/99 Typical Experiment Results Experiment Guide for the PASCO scientific Model ES-9070 COULOMB BALANCE © 1989 PASCO scientific $5.00 012-03760E Coulomb Balance Table of Contents Section Page Copyright, Warranty and Equipment Return...................................................ii Introduction ..................................................................................................... 1 Theory ............................................................................................................. 2 Equipment........................................................................................................ 3 Additional Equipment Recommended: ..................................................... 3 Tips for Accurate Results ................................................................................ 4 Setup ............................................................................................................. 5 Experiments: Part A Force Versus Distance................................................................... 7 Part B Force Versus Charge ...................................................................... 8 Part C The Coulomb Constant ................................................................... 9 Replacing the Torsion Wire........................................................................... 13 Teacher’s Guide............................................................................................. 15 Technical Support
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I. Electric Charge I
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Copyrighted Material
40235_Index_1-9 7/20/01 5:15 PM Page 1 INDEX A orbital, 1067 periodic, 1083–1086 Betatron, 786 Absorption, photon, 1093 spin, 1070–1071 rules of, 1082–1083 Big bang cosmology Accelerator(s) and uncertainty principle, subshell states of, 1071 age determination of universe in, cyclotron, 731–733 1068–1069 x-ray spectrum of, 1079–1081 1192–1194 electrostatic, 651–652 Angular momentum quantum Atomic magnetism, 805–806, expansion of universe in, Acceptor atom, 1113 number, 1067 1086–1087 1186–1187 Actinides, 1083 Anisotropic materials, optically, and atomic radiation, heavy element formation in, Action at a distance, 588 1004 1090–1092 1191–1192 Adiabatic demagnetization, 809 Annihilation, 1188 Atomic mass unit, energy nucleosynthesis in, 1190–1191 Airy disk, 970 Antenna, 866 equivalent of, 1133 particle interactions in, Alpha decay, 1136–1138 Anticoincidence(s), 1023 Atomic number, 570, 602, 603, 1187–1190 Alternating current (AC), Anticoincidence apparatus, 1131. See also Quantum Binding energy, 637, 1133–1134 782–783, 845–846 1023–1024 number(s) Binding energy curve, 1133–1134 transformers of, 852–854 Antineutrino, 1138–1139, and order of elements, Binnig, Gerd, 1047, 1048 and voltages, phase and 1176–1177 1081–1082 Bioluminescence, 886 amplitude relations for, Antineutron, 1178 origin of concept of, 1081 Biot-Savart law, 753 848t Antiparticles, 570 and periodicity of elements, applications of, 753–755 Alternating current circuit Antiproton, 1178 1083–1086 Birefringence, 1005–1006 capacitive element of, 847–848 Atom(s), 1062 Atomic radiation,
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Electric Field Lines
Giambattista College Physics Chapter 16 ©2020 McGraw-Hill Education. All rights reserved. Authorized only for instructor use in the classroom. No reproduction or further distribution permitted without the prior written consent of McGraw-Hill Education. Chapter 16: Electric Forces and Fields 16.1 Electric Charge. 16.2 Electric Conductors and Insulators. 16.3 Coulomb’s “law”. 16.4 The Electric Field. 16.5 Motion of a Point Charge in a Uniform Electric Field. 16.6 Conductors in Electrostatic Equilibrium. 16.7 Gauss’s “law” for Electric Fields. ©2020 McGraw-Hill Education 16.1 Electric Charge 1 Until the invention of the battery (Alessandro Volta) electricity experiments were basically static electricity, like when your clothes cling out of the dryer or you shock yourself after walking across a carpet. One early worker was Benjamin Franklin (1750s). In his book on electricity, he describes: ● killing turkeys ● Proposes execution ● Knocked down up to 6 men holding hands (by essentially building up charge by rubbing) ©2020 McGraw-Hill Education 16.1 Electric Charge 2 A fluid model of electricity proposed that when you rub, you move charge FROM one object TO another, so the NET amount was fixed. (Franklin, et al., proposed ONLY one fluid). So as you rubbed objects together, there was a DEFICIT of charge on one and an EXCESS on the other: Neutral Thing 1 Thing 2 - Charge moves + (not really) ©2020 McGraw-Hill Education 16.1 Electric Charge 2 “Whenever a physicists makes a 50/50 guess, they’ll be wrong about 90% of the time” Dr Wm Deering, UNT MUCH later experiments showed a need for TWO kinds of charge J J Thomson (1897) showed there was a negatively charged particle called the electron.
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Physical Units, Constants and Conversion Factors
Physical Units, Constants and Conversion Factors Here we regroup the values of the most useful physical and chemical constants used in the book. Also some practical combinations of such constants are provided. Units are expressed in the International System (SI), and conversion to the older CGS system is also given. For most quantities and units, the practical deﬁnitions currently used in the context of biophysics are also shown. © Springer International Publishing Switzerland 2016 609 F. Cleri, The Physics of Living Systems, Undergraduate Lecture Notes in Physics, DOI 10.1007/978-3-319-30647-6 610 Physical units, constants and conversion factors Basic physical units (boldface indicates SI fundamental units) SI cgs Biophysics Length (L) meter (m) centimeter (cm) Angstrom (Å) 1 0.01 m 10−10 m Time (T) second (s) second (s) 1 µs=10−6 s 1 1 1ps=10−12 s Mass (M) kilogram (kg) gram (g) Dalton (Da) −27 1 0.001 kg 1/NAv = 1.66 · 10 kg Frequency (T−1) s−1 Hz 1 1 Velocity (L/T) m/s cm/s µm/s 1 0.01 m/s 10−6 m/s Acceleration (L/T2) m/s2 cm/s2 µm/s2 1 0.01 m/s2 10−6 m/s2 Force (ML/T2) newton (N) dyne (dy) pN 1kg· m/s2 10−5 N 10−12 N Energy, work, heat joule (J) erg kB T (at T = 300 K) (ML2/T2) 1kg· m2/s2 10−7 J 4.114 pN · nm 0.239 cal 0.239 · 10−7 cal 25.7 meV 1C· 1V 1 mol ATP = 30.5 kJ = 7.3 kcal/mol Power (ML2/T3) watt (W) erg/s ATP/s 1kg· m2/s3 =1J/s 10−7 J/s 0.316 eV/s Pressure (M/LT2) pascal (Pa) atm Blood osmolarity 1 N/m2 101325˙ Pa ∼ 300 mmol/kg 1 bar = 105 Pa ∼300 Pa = 3 · 10−3 atm Electric current (A) ampere (A) e.s.u.
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