If choose any two different points in the circuit then is the difference of the Potentials at the two points. Entering known values into the expression for the potential of a point charge, we obtain. The electric potential due to a point charge is, thus, a case we need to consider. We can thus determine the excess charge using the equation V = V = k Qr. What is the potential near its surface? 1: A 0.500 cm diameter plastic sphere, used in a static electricity demonstration, has a uniformly distributed 40.0 pC charge on its surface. What Is the Dark Matter We See Indirectly? 11.6 Gauge Pressure, Absolute Pressure, and Pressure Measurement, 82. What is the absolute electric potential of the third charge if , , , m, and m? (i) Equipotential surfaces due to single point charge are concentric sphere having charge at the centre. 27.9 *Extended Topic* Microscopy Enhanced by the Wave Characteristics of Light, 226. Potential due to uniform sphere shows that for a uniform distribution of mass or charge, the potentials outside and inside the sphere are given by V ( r > a) = a r V 0 V ( r a) = 3 a 2 r 2 2 a 2 V 0 where V 0 is the potential at the surface ( r = a). (The radius of the sphere is 12.5 cm.) Example 5.4: Electric potential due to point charges. To find the total electric field, you must add the individual fields as vectors, taking magnitude and direction into account. At infinite, the electric field and the potential are assumed to be zero. As we know that work done is independent of the path choosen. 19.1 Electric Potential Energy: Potential Difference, 146. College Physics by OpenStax is licensed under a Creative Commons Attribution 4.0 International License, except where otherwise noted. citation tool such as, Authors: Paul Peter Urone, Roger Hinrichs. To find the total electric field, you must add the individual fields as vectors, taking magnitude and direction into account. 1: In what region of space is the potential due to a uniformly charged sphere the same as that of a point charge? 3: (a) A sphere has a surface uniformly charged with 1.00 C. At what distance from its center is the potential 5.00 MV? The electric potential V of a point charge is given by. This is a relatively small charge, but it produces a rather large voltage. 6.5 Newtons Universal Law of Gravitation, 40. In what region does it differ from that of a point charge? For a two-charge system with charges q and Q given in the figure above, the change in electric potential energy in taking the charge q, from A to B is given by. 10.4 Rotational Kinetic Energy: Work and Energy Revisited, 71. These forces depend on the direction of the electric field and the charge placed in that field. In this process, potential energy is stored in them. Charges in static electricity are typically in the nanocoulomb nCnC size 12{ left ("nC" right )} {} to microcoulomb CC size 12{ left (C right )} {} range. Furthermore, spherical charge distributions (like on a metal sphere) create external electric fields exactly like a point charge. nC 10.3 Dynamics of Rotational Motion: Rotational Inertia, 70. The voltages in both of these examples could be measured with a meter that compares the measured potential with ground potential. 33.3 Accelerators Create Matter from Energy, 268. 21.6 DC Circuits Containing Resistors and Capacitors, 169. 8.6 Collisions of Point Masses in Two Dimensions, 58. Electric potential of a point charge is [latex]\boldsymbol{V = kQ/r}[/latex]. 30.4 X Rays: Atomic Origins and Applications, 243. What excess charge resides on the sphere? 14.2 Temperature Change and Heat Capacity, 108. The work done is positive in this case. 17.2 Speed of Sound, Frequency, and Wavelength, 130. (b) At what distance from its center is the potential 1.00 MV? 4: How far from a [latex]{1.00 \mu \text{C}}[/latex] point charge will the potential be 100 V? Ground potential is often taken to be zero (instead of taking the potential at infinity to be zero). a) Some positive value Want to create or adapt books like this? Here, q1 = 10 pC = 10 x 10-12C, q2 = -10 pC = -2 x 10-12C and r = 2m. Question 5: Two charges are kept at opposite corners of rectangles as shown in the figure. Potential Due to a Charged Particle Question 2 Detailed Solution CONCEPT : The amount of work done in moving a unit positive charge in an electric field from infinity to that point without accelerating the charge against the direction of the electric field is electrostatic potential. / Furthermore, spherical charge distributions (like on a metal sphere) create external electric fields exactly like a point charge. Thus [latex]\boldsymbol{V}[/latex] for a point charge decreases with distance, whereas [latex]\boldsymbol{E}[/latex] for a point charge decreases with distance squared: Recall that the electric potential [latex]\boldsymbol{V}[/latex] is a scalar and has no direction, whereas the electric field [latex]\textbf{E}[/latex] is a vector. The electric potential is a scalar while the . Share on Whatsapp [/latex], [latex]\begin{array}{r @{{}={}} l} {V} & {k \frac{Q}{r}} \\[1em] & {(8.99 \times 10^9 \;\textbf{N} \cdot \text{m}^2 / \text{C}^2)(\frac{-3.00 \times 10^{9} \;\text{C}}{5.00 \times 10^{2} \;\text{m}})} \\[1em] & {-539 \;\text{V}}. At what distance will it be [latex]\boldsymbol{2.00 \times 10^2 \;\textbf{V}}[/latex]? The electric potential due to a point charge is, thus, a case we need to consider. Test. The voltage of this demonstration Van de Graaff generator is measured between the charged sphere and ground. Suppose, a motorcycle battery and a car battery have the same voltage. Electric forces are experienced by charged bodies when they come under the influence of an electric field. Thus we can find the voltage using the equation [latex]{V = kQ/r}[/latex] . 13.4 Kinetic Theory: Atomic and Molecular Explanation of Pressure and Temperature, 98. Calculate: The electric potential due to the charges at both point A of coordinates (0,1) and B (0,-1). Charges in static electricity are typically in the nanocoulomb (nC) to microcoulomb [latex]\boldsymbol{( \mu \textbf{C})}[/latex] range. In the figure given below, there is a huge plate that is negatively charged, and it has some positive charges stuck on it. (a) What charge is on the sphere? size 12{V= ital "kQ"/r} {}, Entering known values into the expression for the potential of a point charge, we obtain. 30.6 The Wave Nature of Matter Causes Quantization, 245. Thus VV size 12{V} {} for a point charge decreases with distance, whereas EE size 12{E} {} for a point charge decreases with distance squared. 18.5 Electric Field Lines: Multiple Charges, 142. zero. V= 4 01 rq. The potential at infinity is chosen to be zero. Conceptual Questions (Assume that each numerical value here is shown with three significant figures. A silicon nucleus has a charge of +14e, and its radius is about 3.6E-15 m. Assume the potential is that for point charges. (5.12.2) V 21 = r 1 r 2 E d l. Chapter 1 The Nature of Science and Physics, Chapter 4 Dynamics: Force and Newtons Laws of Motion, Chapter 5 Further Applications of Newtons Laws: Friction, Drag and Elasticity, Chapter 6 Uniform Circular Motion and Gravitation, Chapter 7 Work, Energy, and Energy Resources, Chapter 10 Rotational Motion and Angular Momentum, Chapter 12 Fluid Dynamics and Its Biological and Medical Applications, Chapter 13 Temperature, Kinetic Theory, and the Gas Laws, Chapter 14 Heat and Heat Transfer Methods, Chapter 18 Electric Charge and Electric Field, Chapter 20 Electric Current, Resistance, and Ohms Law, Chapter 23 Electromagnetic Induction, AC Circuits, and Electrical Technologies, Chapter 26 Vision and Optical Instruments, Chapter 29 Introduction to Quantum Physics, Chapter 31 Radioactivity and Nuclear Physics, Chapter 32 Medical Applications of Nuclear Physics, [latex]{V =}[/latex] [latex]{\frac{kQ}{r}}[/latex] [latex]{( \text{Point Charge} ),}[/latex], [latex]{E =}[/latex] [latex]{\frac{F}{q}}[/latex] [latex]{=}[/latex] [latex]{\frac{kQ}{r^2}}. Electric Potential and Derivation of Electric Potential at a Point due to Point Charged Particle Electric Potential: When a test charged particle is brought from infinity to a point in the electric field then the work done per unit test charge particle is called electric potential. The positive charge is near the plate, the farther the charge is from this plate, the more the work done on the charge. (a) What is the potential near its surface? To find the voltage due to a combination of point charges, you add the individual voltages as numbers. 21.1 Resistors in Series and Parallel, 162. The OpenStax name, OpenStax logo, OpenStax book covers, OpenStax CNX name, and OpenStax CNX logo Notice that in the figure, there are some concentric circles. The charge placed at that point will exert a force due to the presence of an electric field. 16.10 Superposition and Interference, 129. This is consistent with the fact that [latex]\boldsymbol{V}[/latex] is closely associated with energy, a scalar, whereas [latex]\textbf{E}[/latex] is closely associated with force, a vector. Electric Potential Formula Method 1: The electric potential at any point around a point charge q is given by: V = k [q/r] Where, V = electric potential energy q = point charge r = distance between any point around the charge to the point charge k = Coulomb constant; k = 9.0 10 9 N Method 2: Using Coulomb's Law 9.1 The First Condition for Equilibrium, 61. 16.1 Hookes Law: Stress and Strain Revisited, 117. are not subject to the Creative Commons license and may not be reproduced without the prior and express written 22.11 More Applications of Magnetism, 181. 5: What are the sign and magnitude of a point charge that produces a potential of [latex]\boldsymbol{-2.00 \;\textbf{V}}[/latex] at a distance of 1.00 mm? (c) The assumption that the speed of the electron is far less than that of light and that the problem does not require a relativistic treatment produces an answer greater than the speed of light. The potential of the charged conducting sphere is the same as that of an equal point charge at its center. To find the voltage due to a combination of point charges, you add the individual voltages as numbers. The electric potential V V of a point charge is given by. Thus [latex]{V}[/latex] for a point charge decreases with distance, whereas [latex]{E}[/latex] for a point charge decreases with distance squared: Recall that the electric potential [latex]{V}[/latex] is a scalar and has no direction, whereas the electric field [latex]\textbf{E}[/latex] is a vector. Using calculus to find the work needed to move a test charge [latex]\boldsymbol{q}[/latex] from a large distance away to a distance of [latex]\boldsymbol{r}[/latex] from a point charge [latex]\boldsymbol{Q}[/latex], and noting the connection between work and potential [latex]\boldsymbol{(W = -q \Delta V)}[/latex], it can be shown that the electric potential [latex]\boldsymbol{V}[/latex] of a point charge is, where k is a constant equal to [latex]\boldsymbol{9.0 \times 10^9 \;\textbf{N} \cdot \textbf{m}^2 / \textbf{C}^2 . For an isolated point charge:Potential at a distance r due to point charge +q. 1: In what region of space is the potential due to a uniformly charged sphere the same as that of a point charge? Terms in this set (25) r = diameter/2 r = 0.340/2 cm = 0.0017m . Here, q1 = 1 pC = 10-12C, q2 = -2 pC = -2 x 10-12C and r1 = 2m and r2 = 1m. School Guide: Roadmap For School Students, Data Structures & Algorithms- Self Paced Course, Electric Charge and Electric Field - Electric Flux, Coulomb's Law, Sample Problems, Electric Potential Due to System of Charges, Difference Between Electric Potential and Potential Difference, Electric Charge - Definition, History, Types and Properties, Electric Field due to Infinitely Long Straight Wire, Electric Field due to Uniformly Charged Infinite Plane Sheet and Thin Spherical Shell. 30.7 Patterns in Spectra Reveal More Quantization, 250. . 20.5 Alternating Current versus Direct Current, 158. 33.1 The Yukawa Particle and the Heisenberg Uncertainty Principle Revisited, 267. Electric forces are responsible for almost every chemical reaction within the human body. The electric potential due to a point charge is, thus, a case we need to consider. What is the voltage 5.00 cm away from the center of a 1-cm diameter metal sphere that has a 3.00nC3.00nC static charge? So, in this situation, the potential energy stored in these charges is converted into kinetic energy. (b) What charge must a 0.100-mg drop of paint have to arrive at the object with a speed of 10.0 m/s? Ground potential is often taken to be zero (instead of taking the potential at infinity to be zero). Now lets understand the potential due to a point charge in formal terms. Explain point charges and express the equation for electric potential of a point charge. Textbook content produced by OpenStax is licensed under a Creative Commons Attribution License . (b) What is the potential energy in MeV of a similarly charged fragment at this distance? So option 4 is correct. k Q r. 6.1 Rotation Angle and Angular Velocity, 38. 16.3 Simple Harmonic Motion: A Special Periodic Motion, 120. V = V = kQ r k Q r (Point Charge), ( Point Charge), The potential at infinity is chosen to be zero. 4. In what region does it differ from that of a point charge? Using calculus to find the work needed to move a test charge q from a large distance away to a distance of r from a point charge Q, and noting the connection between work and potential (W = - q V), it can be shown that the electric potential V of a point . Electric potential at a point in space. The electric potential at a point in free space due to a charge Q coulomb is Q10 11V. 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The voltages in both of these examples could be measured with a meter that compares the measured potential with ground potential. Potential Energy in an External Field (i) Potential Energy of a single charge in external field Potential energy of a single charge q at a point with position vector r, in an external field is qV(r), where V(r) is the potential at the point due to external electric field E. 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The electric potential at a point is equal to the electric potential energy (measured in joules) of any charged particle at that location divided by the charge (measured in coulombs) of the particle. 20.7 Nerve ConductionElectrocardiograms, 161. 4. By using our site, you Physics questions and answers The electric potential due to a point charge approaches zero as you move farther away from the charge. 16.6 Uniform Circular Motion and Simple Harmonic Motion, 123. 7: In nuclear fission, a nucleus splits roughly in half. Hence, the net electric potential at point B is .negative. We can thus determine the excess charge using the equation, Solving for What excess charge resides on the sphere? Recall that the electric potential . Except where otherwise noted, textbooks on this site If the three point charges shown here lie at the vertices of an equilateral triangle, the electric potential at the center of the triangle is positive. Conversely, a negative charge would be repelled, as expected. In this process, some molecules are formed and some change their shape. 7.2 Kinetic Energy and the Work-Energy Theorem, 45. 4.8 Extended Topic: The Four Basic ForcesAn Introduction, 35. As the unit of electric potential is volt, 1 Volt (V) = 1 joule coulomb-1(JC-1) At the point when work is done in moving a charge of 1 coulomb from infinity to a specific point because of an electric field against . We will calculate electric potential at any point P due to a single point charge +q at O ;where OP=r. 5:[latex]{-2.22 \times 10^{-13} \;\text{C}}[/latex], 7: (a) [latex]{3.31 \times 10^6 \;\text{V}}[/latex], 9: (a) [latex]{2.78 \times 10^{-7} \;\text{C}}[/latex], (b) [latex]{2.00 \times 10^{-10} \;\text{C}}[/latex], 12: (a) [latex]{2.96 \times 10^9 \;\text{m}/ \text{s}}[/latex]. To find the total electric field, you must add the individual fields as vectors, taking magnitude and direction into account. 1999-2022, Rice University. Explain point charges and express the equation for electric potential of a point charge. To check the difference in the electric potential between two positions under the influence of an electric field, it is asked, how much the potential energy of a unit positive charge will change if that charge is moved from this position to the other position. 22.4 Magnetic Field Strength: Force on a Moving Charge in a Magnetic Field, 172. When charges are moved around in the electric field, these forces do work on the charge and that gets stored in the form of electrostatic potential energy. So we'll have 2250 joules per coulomb plus 9000 joules per coulomb plus negative 6000 joules per coulomb. (easy) Refer to the scenario in question #1. a. One of the points in the circuit can be always designated as the zero potential point. V = 40 ln( a2 + r2 +a a2 + r2-a) V = 4 0 ln ( a 2 + r 2 + a a . As noted in Electric Potential Energy: Potential Difference, this is analogous to taking sea level as h=0h=0 size 12{h=0} {} when considering gravitational potential energy, PEg=mgh.PEg=mgh. Electrostatic potential energy of charge 'q' at a point is the work done by the external force in bringing the charge 'q' from infinity to that point. 9: An electrostatic paint sprayer has a 0.200-m-diameter metal sphere at a potential of 25.0 kV that repels paint droplets onto a grounded object. Thus we can find the voltage using the equation [latex]\boldsymbol{V = kQ/r}[/latex] . What is the voltage 5.00 cm away from the center of a 1-cm diameter metal sphere that has a Definition. 15.6 Entropy and the Second Law of Thermodynamics: Disorder and the Unavailability of Energy, 114. The negative value for voltage means a positive charge would be attracted from a larger distance, since the potential is lower (more negative) than at larger distances. 15.5 Applications of Thermodynamics: Heat Pumps and Refrigerators, 113. Or Why Dont All Objects Roll Downhill at the Same Rate? We can thus determine the excess charge using the equation V = V = kQ r. k Q r. (b) What does your answer imply about the practical aspect of isolating such a large charge? 32.1 Medical Imaging and Diagnostics, 258. The potential of the charged conducting sphere is the same as that of an equal point charge at its center. Determine the electric potential of a point charge given charge and distance. 23.2 Faradays Law of Induction: Lenzs Law, 183. The negative value for voltage means a positive charge would be attracted from a larger distance, since the potential is lower (more negative) than at larger distances. 5: What are the sign and magnitude of a point charge that produces a potential of [latex]{-2.00 \;\text{V}}[/latex] at a distance of 1.00 mm? We have derived the potential for a line of charge of length 2a in Electric Potential Of A Line Of Charge. The Electrostatic Potential due to point charge is the amount of work needed to move a unit of electric charge from a reference point to a specific point in an electric field without producing an acceleration and is represented as V = [Coulomb]*q/r or Electrostatic Potential = [Coulomb]*Charge/Separation between Charges. Here you can find the meaning of Calculate electric potential due to a point charge of 10C at a distance of 8cm away from the charge.a)1.125*1013Vb)1.125*1012Vc)2.25*1013Vd)0.62*1013VCorrect answer is option 'B'. 8.4 Elastic Collisions in One Dimension, 56. (easy) Is the magnitude of the electric potential caused by point charges an absolute or a relative value. Electric Potential Question 1: Due to a point charge of 4 10-7 C, . For a system of point charges, the total potential at a point is given by the algebraic sum of the potential for individual charges at that point. (See Figure 1.) Electric potential is a scalar, and electric field is a vector. (ii) In constant electric field along z-direction, the perpendicular distance between equipotential surfaces remains same. then you must include on every digital page view the following attribution: Use the information below to generate a citation. Here, q = 10 pC = 10 x 10-12C and r = 0.5m. The electric potential tells you how much potential energy a single point charge at a given location will have. V = V = kQ r k Q r (Point Charge), ( Point Charge), The potential at infinity is chosen to be zero. Thus V V for a point charge decreases with distance, whereas E E for a point charge decreases with distance squared: E = E = F q F q = = kQ r2. 34.2 General Relativity and Quantum Gravity, 277. With a surge in distance from electric dipole, the effects of positive and negative charges will nullify each other. Potential due to point charges Calculating the point where potential V = 0 (due to 2 charges) Last Post; May 13, 2022; Replies 2 Views 234. Match. (ii) Potential, due to an electric dipole (length 2a) varies as the inverse square' of the distance of the 'field point' from the centre of the dipole for r > a. The electric field intensity due to a point charge q at the origin is (see Section 5.1 or 5.5) (5.12.1) E = r ^ q 4 r 2. Two point charges q 1 = q 2 = 10 -6 C are located respectively at coordinates (-1, 0) and (1, 0) (coordinates expressed in meters). UY1: Electric Potential Of An Infinite Line Charge. 2.39 E = F q = kQ r2. Share Cite Improve this answer Follow 10.6 Collisions of Extended Bodies in Two Dimensions, 73. 1.3 Accuracy, Precision, and Significant Figures, 2.2 Vectors, Scalars, and Coordinate Systems, 2.5 Motion Equations for Constant Acceleration in One Dimension, 2.6 Problem-Solving Basics for One-Dimensional Kinematics, 2.8 Graphical Analysis of One-Dimensional Motion, 3.1 Kinematics in Two Dimensions: An Introduction, 3.2 Vector Addition and Subtraction: Graphical Methods, 3.3 Vector Addition and Subtraction: Analytical Methods, 4.2 Newtons First Law of Motion: Inertia, 4.3 Newtons Second Law of Motion: Concept of a System, 4.4 Newtons Third Law of Motion: Symmetry in Forces, 4.5 Normal, Tension, and Other Examples of Forces, 4.7 Further Applications of Newtons Laws of Motion, 4.8 Extended Topic: The Four Basic ForcesAn Introduction, 6.4 Fictitious Forces and Non-inertial Frames: The Coriolis Force, 6.5 Newtons Universal Law of Gravitation, 6.6 Satellites and Keplers Laws: An Argument for Simplicity, 7.2 Kinetic Energy and the Work-Energy Theorem, 7.4 Conservative Forces and Potential Energy, 8.5 Inelastic Collisions in One Dimension, 8.6 Collisions of Point Masses in Two Dimensions, 9.4 Applications of Statics, Including Problem-Solving Strategies, 9.6 Forces and Torques in Muscles and Joints, 10.3 Dynamics of Rotational Motion: Rotational Inertia, 10.4 Rotational Kinetic Energy: Work and Energy Revisited, 10.5 Angular Momentum and Its Conservation, 10.6 Collisions of Extended Bodies in Two Dimensions, 10.7 Gyroscopic Effects: Vector Aspects of Angular Momentum, 11.4 Variation of Pressure with Depth in a Fluid, 11.6 Gauge Pressure, Absolute Pressure, and Pressure Measurement, 11.8 Cohesion and Adhesion in Liquids: Surface Tension and Capillary Action, 12.1 Flow Rate and Its Relation to Velocity, 12.3 The Most General Applications of Bernoullis Equation, 12.4 Viscosity and Laminar Flow; Poiseuilles Law, 12.6 Motion of an Object in a Viscous Fluid, 12.7 Molecular Transport Phenomena: Diffusion, Osmosis, and Related Processes, 13.2 Thermal Expansion of Solids and Liquids, 13.4 Kinetic Theory: Atomic and Molecular Explanation of Pressure and Temperature, 14.2 Temperature Change and Heat Capacity, 15.2 The First Law of Thermodynamics and Some Simple Processes, 15.3 Introduction to the Second Law of Thermodynamics: Heat Engines and Their Efficiency, 15.4 Carnots Perfect Heat Engine: The Second Law of Thermodynamics Restated, 15.5 Applications of Thermodynamics: Heat Pumps and Refrigerators, 15.6 Entropy and the Second Law of Thermodynamics: Disorder and the Unavailability of Energy, 15.7 Statistical Interpretation of Entropy and the Second Law of Thermodynamics: The Underlying Explanation, 16.1 Hookes Law: Stress and Strain Revisited, 16.2 Period and Frequency in Oscillations, 16.3 Simple Harmonic Motion: A Special Periodic Motion, 16.5 Energy and the Simple Harmonic Oscillator, 16.6 Uniform Circular Motion and Simple Harmonic Motion, 17.2 Speed of Sound, Frequency, and Wavelength, 17.5 Sound Interference and Resonance: Standing Waves in Air Columns, 18.1 Static Electricity and Charge: Conservation of Charge, 18.4 Electric Field: Concept of a Field Revisited, 18.5 Electric Field Lines: Multiple Charges, 18.7 Conductors and Electric Fields in Static Equilibrium, 19.1 Electric Potential Energy: Potential Difference, 19.2 Electric Potential in a Uniform Electric Field, 19.3 Electrical Potential Due to a Point Charge, 20.2 Ohms Law: Resistance and Simple Circuits, 20.5 Alternating Current versus Direct Current, 21.2 Electromotive Force: Terminal Voltage, 21.6 DC Circuits Containing Resistors and Capacitors, 22.3 Magnetic Fields and Magnetic Field Lines, 22.4 Magnetic Field Strength: Force on a Moving Charge in a Magnetic Field, 22.5 Force on a Moving Charge in a Magnetic Field: Examples and Applications, 22.7 Magnetic Force on a Current-Carrying Conductor, 22.8 Torque on a Current Loop: Motors and Meters, 22.9 Magnetic Fields Produced by Currents: Amperes Law, 22.10 Magnetic Force between Two Parallel Conductors, 23.2 Faradays Law of Induction: Lenzs Law, 23.8 Electrical Safety: Systems and Devices, 23.11 Reactance, Inductive and Capacitive, 24.1 Maxwells Equations: Electromagnetic Waves Predicted and Observed, 27.1 The Wave Aspect of Light: Interference, 27.6 Limits of Resolution: The Rayleigh Criterion, 27.9 *Extended Topic* Microscopy Enhanced by the Wave Characteristics of Light, 29.3 Photon Energies and the Electromagnetic Spectrum, 29.7 Probability: The Heisenberg Uncertainty Principle, 30.2 Discovery of the Parts of the Atom: Electrons and Nuclei, 30.4 X Rays: Atomic Origins and Applications, 30.5 Applications of Atomic Excitations and De-Excitations, 30.6 The Wave Nature of Matter Causes Quantization, 30.7 Patterns in Spectra Reveal More Quantization, 32.2 Biological Effects of Ionizing Radiation, 32.3 Therapeutic Uses of Ionizing Radiation, 33.1 The Yukawa Particle and the Heisenberg Uncertainty Principle Revisited, 33.3 Accelerators Create Matter from Energy, 33.4 Particles, Patterns, and Conservation Laws, 34.2 General Relativity and Quantum Gravity, Appendix D Glossary of Key Symbols and Notation, Chapter 19 Electric Potential and Electric Field, Point charges, such as electrons, are among the fundamental building blocks of matter. 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