DOCSLIB.ORG

Electricity • Charge • Coulomb Force • Electric Field

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Electricity • Charge • Coulomb Force • Electric Field List of important topics: Electricity • Charge • Coulomb Force • Electric field • Electric potential (volt) • Voltage sources (potential difference, conductors) • Electric current • Ohm’s law • Circuits (series, parallel, diagrams, overloading) • Power Magnets • Poles N,S • Fields • Materials (iron, regions) • Currents è Magnets • E çè M (forces, meters, motors) • E çè M induction (Faraday’s law: E field induced by changing B) • Generators, alternators • Power production • Tranformers • E çè M B field induced by changing E Week 9 Next period General E&M theory • fields • Electric • Magnetic • relationship (electromagnets è an effect that links these 2 forces Fundamental Electric Forceè Coulomb’ law • charges • attraction repulsion • static electricity !!∗!! • � = � � !! o depends inversely on the distance squared o depends on the magnitude of each charge o signs of the charges determine direction o force is a vector o direction is shown as � [called a unit vector] !!∗!! o � is used to calculate the magnitude or strength of the force !! We want to understand that there is a fundamental view of nature that establishes what matter is and how matter interacts. These underpinnings are theoretically supposed to explain much of what we see and experience. However, it is extremely difficult to calculate general phenomena directly from first principles. Scientists have developed steps that start at the basic tenets and then show that they are valid for simple systems. The approach is then to extract the fundamental and critical parts and apply them in the form of a model. The result is a valid description at all levels that stems from the basic tenets but is not a direct calculation of the behavior. For example: Most chemists use molecular and atomic models that predict chemical behavior. The idea of covalent and ionic bonding along with some other ingredients suffices to maKe very powerful predictive tools. The actual fundamental calculation using positively charged cores (nuclei) surrounded by negatively charged electrons interacting through the E&M force is intractable. A problem that can be solved is the hydrogen atom that consists of only 2 particles. This system has been studied and calculations match theory at a precision of 1ppm. This is a clear verification that the underlying theory is a good approximation to reality and extrapolations to chemistry should be able to model complex systems by extracting and applying the Key elements of the theory. It is important to understand this hierarchy in science. Models based on our understanding of basic principles but employing simplifications and extracting critical factors are the trademarKs of science. No one expects to predict cell behavior by using particle physics. However, cell behavior should never violate conservation of energy. Fundamental theory: • Matter consists of groupings of elementary particles. The current list of particles that seem to exhibit this label (elementary or fundamental) are: electrons, quarKs (u,d), muons ….. • Our world is primarily made from quarKs that combine to produce protons and neutrons. Electrons, protons, neutron constitute the basic building blocks for much of what we experience. Although protons and neutrons are not really fundamental because they are composite systems of quarks. the internal nature doesn’t reveal itself for most matter and is irrelevant to the majority of chemistry and material properties in which we are interested. {We did discuss carbon dating and radioactive decay of isotopes. To understand these processes we do need to consider the quarK maKe up of the neutron. In this class Knowing that isotope decay via radioactive processes suffices. No understanding of the underlying theory is expected.} • Matter interacts via 4 fundamental forces or interactions: o gravity (mass and distance) o E&M (charge, motion of charge, distance) o Weak (responsible for neutron decay, not usually relevant) o Strong (hold protons and neutrons in closely packed arrays as nuclei) So to understand why books are supported on a table and why we can live in an atmosphere filled with material (air), we recogniZe that atoms are the basic structures of matter. • Atoms consist of a nucleus surrounded by electrons. The negative electrons are bound to the positive nuclei primarily due to the electric force of attraction between charges. o Atoms are labeled by the number of protons in the nucleus o Isotopes are nuclei that have the same number of protons but different numbers of neutrons. o Usually only one isotope is stable and therefore remains unchanged while other isotopes eventually transition to the stable form. § Discussed C14 and C12 as an example of isotopes and described how carbon dating is achieved by measuring the loss of C14 due to its decay. • Atoms combine to maKe molecules. The electric force is still the essential ingredient in understanding molecule formation. [ Quantum mechanics is also essential for our understanding of molecules and atoms but we will not need to worry about these details.] Electricity magnetism E&M is a complex fundamental interaction. This interaction is responsible for most of the features we experience in our world. Basis for atoms and molecules. Determines material properties and interactions. Most phenomena (excluding gravity, falling and earth-sun-moon binding) can be seen as an E&M interaction. 2 charges +,- N,S Electron è - , point particle No individual N or S poles found Protonè + , made of quarKs Due to electric currents q q Same characteristics as electric force 1 2 ˆ F = k 2 r r only for N,S poles drops with distance act along line joining charges like repel, unlike attract € r=distance between charges rˆ = unit vector it shows direction only q q k 1 2 = provides magnitude of force, r2 sign € + means repulsion, neg means attraction € While originally the interactions in the columns appeared similar they were considered to be distinct, unrelated interactions. However, the forces were linked when electric currents were found to have magnetic interactions (electromagnet). Electric current Measured in Amps A Flow Amount of charge that passes through an imaginary slice in a wire per second 1 A = 1 C/s Analogs: water flows in rivers (flowè amount passes by per second Flow of cars on highway (flowè # cars pass under bridge per second Therefore flow depends on two quantities speed, amount Few cars traveling fast = high flow Many cars traveling slow high flow Flow at 2:00 AM (90 MPH) i.e. the # under the bridge in a given time can be the same as the flow for a traffic jam (1 MPH). Mississippi can have slow moving sections where the river is wide and faster sections where the river is narrow but the flow is the same. Voltage Push that causes the flow Analog: For rivers flow is due to gravity è Flowing down hill Analog: For sKiers its due to gravity (vertical drop) Analog: Gravity can be used to propel material along a path the amount of push can be related to the height h. In trying to understand voltage we can consider things that flow down hill due to gravity. We can also identify the height that a skier descends or a river traverses as an important factor in determining flow. Indeed we can imagine that voltage can be directly linKed to the height for a system that has material flowing due to gravity. This linK allows us to develop some intuition about voltage and voltage distribution in a circuit. Students are not required to know the details of Maxwell’s equations or the general force law as shown in the following aside. Aside è Fundamental structure of E&M Maxwell's equations are a set of partial differential equations that, together with the Lorentz force law, form the foundation of classical electrodynamics, classical optics, and electric circuits. F = qE + qv × B Lorentz force Formulation in terms of total charge and current, differential form SI UNITS € Name Differential form Gauss's law Gauss's law for magnetism Maxwell–Faraday equation (Faraday's law of induction) Ampère's circuital law (with Maxwell's correction) Formulation in terms of total charge and current, integral form SI UNITS Name Integral form Gauss's law Gauss's law for magnetism Maxwell–Faraday equation (Faraday's law of induction) Ampère's circuital law (with Maxwell's correction) . A qualitative understanding of each law is important and provided below. Define the field in terms of the force experienced per unit source General force law è F = qE + qv × B Lorentz force. For electric charge we can see the field is the force per unit charge. F E = q € The test charge should not be moving in orde r to eliminate interactions with the magnetic field. € Gauss’s law There is a force between electric charges that satisfies Coulomb’s E law (with the Lorentz Force) Gauss’s law Same for magnets (no fundamental monopoles) B Faraday A changing magnetic field induces and electric field. A magnet equation pushed and pulled through a loop of wire drives a current around the loop. Since there are no monopoles there is no “magnetic analog of current”. All N, S are ultimately created by moving electric charge so fundamental fields are generated ultimately by electric charge. Ampere’s -Currents produce magnetic fields law with -Changing electric fields produce magnetic fields. displacement current. Field- Let us taKe the definition of the field and find the field at some points, Postive point charge Electric dipole field Parallel plate capacitor (plates must be large compared to the gap) Magnetic field of a wire (What field does an electric current generate ß Ampere’s Law Magnetic field of a loop Magnetic field of a coil N-S dipole field Several loop coil field Electric charge moving in a circular path can produce a similar “external” field as that due to a N-S dipole.
Load more

Recommended publications
  • The Lorentz Force
    CLASSICAL CONCEPT REVIEW 14 The Lorentz Force We can find empirically that a particle with mass m and electric charge q in an elec- tric field E experiences a force FE given by FE = q E LF-1 It is apparent from Equation LF-1 that, if q is a positive charge (e.g., a proton), FE is parallel to, that is, in the direction of E and if q is a negative charge (e.g., an electron), FE is antiparallel to, that is, opposite to the direction of E (see Figure LF-1). A posi- tive charge moving parallel to E or a negative charge moving antiparallel to E is, in the absence of other forces of significance, accelerated according to Newton’s second law: q F q E m a a E LF-2 E = = 1 = m Equation LF-2 is, of course, not relativistically correct. The relativistically correct force is given by d g mu u2 -3 2 du u2 -3 2 FE = q E = = m 1 - = m 1 - a LF-3 dt c2 > dt c2 > 1 2 a b a b 3 Classically, for example, suppose a proton initially moving at v0 = 10 m s enters a region of uniform electric field of magnitude E = 500 V m antiparallel to the direction of E (see Figure LF-2a). How far does it travel before coming (instanta> - neously) to rest? From Equation LF-2 the acceleration slowing the proton> is q 1.60 * 10-19 C 500 V m a = - E = - = -4.79 * 1010 m s2 m 1.67 * 10-27 kg 1 2 1 > 2 E > The distance Dx traveled by the proton until it comes to rest with vf 0 is given by FE • –q +q • FE 2 2 3 2 vf - v0 0 - 10 m s Dx = = 2a 2 4.79 1010 m s2 - 1* > 2 1 > 2 Dx 1.04 10-5 m 1.04 10-3 cm Ϸ 0.01 mm = * = * LF-1 A positively charged particle in an electric field experiences a If the same proton is injected into the field perpendicular to E (or at some angle force in the direction of the field.
    [Show full text]
  • Capacitance and Dielectrics Capacitance
    Capacitance and Dielectrics Capacitance General Definition: C === q /V Special case for parallel plates: εεε A C === 0 d Potential Energy • I must do work to charge up a capacitor. • This energy is stored in the form of electric potential energy. Q2 • We showed that this is U === 2C • Then we saw that this energy is stored in the electric field, with a volume energy density 1 2 u === 2 εεε0 E Potential difference and Electric field Since potential difference is work per unit charge, b ∆∆∆V === Edx ∫∫∫a For the parallel-plate capacitor E is uniform, so V === Ed Also for parallel-plate case Gauss’s Law gives Q Q εεε0 A E === σσσ /εεε0 === === Vd so C === === εεε0 A V d Spherical example A spherical capacitor has inner radius a = 3mm, outer radius b = 6mm. The charge on the inner sphere is q = 2 C. What is the potential difference? kq From Gauss’s Law or the Shell E === Theorem, the field inside is r 2 From definition of b kq 1 1 V === dr === kq −−− potential difference 2 ∫∫∫a r a b 1 1 1 1 === 9 ×××109 ××× 2 ×××10−−−9 −−− === 18 ×××103 −−− === 3 ×××103 V −−−3 −−−3 3 ×××10 6 ×××10 3 6 What is the capacitance? C === Q /V === 2( C) /(3000V ) === 7.6 ×××10−−−4 F A capacitor has capacitance C = 6 µF and charge Q = 2 nC. If the charge is Q.25-1 increased to 4 nC what will be the new capacitance? (1) 3 µF (2) 6 µF (3) 12 µF (4) 24 µF Q.
    [Show full text]
  • Chapter 5 Capacitance and Dielectrics
    Chapter 5 Capacitance and Dielectrics 5.1 Introduction...........................................................................................................5-3 5.2 Calculation of Capacitance ...................................................................................5-4 Example 5.1: Parallel-Plate Capacitor ....................................................................5-4 Interactive Simulation 5.1: Parallel-Plate Capacitor ...........................................5-6 Example 5.2: Cylindrical Capacitor........................................................................5-6 Example 5.3: Spherical Capacitor...........................................................................5-8 5.3 Capacitors in Electric Circuits ..............................................................................5-9 5.3.1 Parallel Connection......................................................................................5-10 5.3.2 Series Connection ........................................................................................5-11 Example 5.4: Equivalent Capacitance ..................................................................5-12 5.4 Storing Energy in a Capacitor.............................................................................5-13 5.4.1 Energy Density of the Electric Field............................................................5-14 Interactive Simulation 5.2: Charge Placed between Capacitor Plates..............5-14 Example 5.5: Electric Energy Density of Dry Air................................................5-15
    [Show full text]
  • Electric Potential
    Electric Potential • Electric Potential energy: b U F dl elec elec a • Electric Potential: b V E dl a Field is the (negative of) the Gradient of Potential dU dV F E x dx x dx dU dV F UF E VE y dy y dy dU dV F E z dz z dz In what direction can you move relative to an electric field so that the electric potential does not change? 1)parallel to the electric field 2)perpendicular to the electric field 3)Some other direction. 4)The answer depends on the symmetry of the situation. Electric field of single point charge kq E = rˆ r2 Electric potential of single point charge b V E dl a kq Er ˆ r 2 b kq V rˆ dl 2 a r Electric potential of single point charge b V E dl a kq Er ˆ r 2 b kq V rˆ dl 2 a r kq kq VVV ba rrba kq V const. r 0 by convention Potential for Multiple Charges EEEE1 2 3 b V E dl a b b b E dl E dl E dl 1 2 3 a a a VVVV 1 2 3 Charges Q and q (Q ≠ q), separated by a distance d, produce a potential VP = 0 at point P. This means that 1) no force is acting on a test charge placed at point P. 2) Q and q must have the same sign. 3) the electric field must be zero at point P. 4) the net work in bringing Q to distance d from q is zero.
    [Show full text]
  • Physics 2102 Lecture 2
    Physics 2102 Jonathan Dowling PPhhyyssicicss 22110022 LLeeccttuurree 22 Charles-Augustin de Coulomb EElleeccttrriicc FFiieellddss (1736-1806) January 17, 07 Version: 1/17/07 WWhhaatt aarree wwee ggooiinngg ttoo lleeaarrnn?? AA rrooaadd mmaapp • Electric charge Electric force on other electric charges Electric field, and electric potential • Moving electric charges : current • Electronic circuit components: batteries, resistors, capacitors • Electric currents Magnetic field Magnetic force on moving charges • Time-varying magnetic field Electric Field • More circuit components: inductors. • Electromagnetic waves light waves • Geometrical Optics (light rays). • Physical optics (light waves) CoulombCoulomb’’ss lawlaw +q1 F12 F21 !q2 r12 For charges in a k | q || q | VACUUM | F | 1 2 12 = 2 2 N m r k = 8.99 !109 12 C 2 Often, we write k as: 2 1 !12 C k = with #0 = 8.85"10 2 4$#0 N m EEleleccttrricic FFieieldldss • Electric field E at some point in space is defined as the force experienced by an imaginary point charge of +1 C, divided by Electric field of a point charge 1 C. • Note that E is a VECTOR. +1 C • Since E is the force per unit q charge, it is measured in units of E N/C. • We measure the electric field R using very small “test charges”, and dividing the measured force k | q | by the magnitude of the charge. | E |= R2 SSuuppeerrppoossititioionn • Question: How do we figure out the field due to several point charges? • Answer: consider one charge at a time, calculate the field (a vector!) produced by each charge, and then add all the vectors! (“superposition”) • Useful to look out for SYMMETRY to simplify calculations! Example Total electric field +q -2q • 4 charges are placed at the corners of a square as shown.
    [Show full text]
  • Frequency Dependence of the Permittivity
    Frequency dependence of the permittivity February 7, 2016 In materials, the dielectric “constant” and permeability are actually frequency dependent. This does not affect our results for single frequency modes, but when we have a superposition of frequencies it leads to dispersion. We begin with a simple model for this behavior. The variation of the permeability is often quite weak, and we may take µ = µ0. 1 Frequency dependence of the permittivity 1.1 Permittivity produced by a static field The electrostatic treatment of the dielectric constant begins with the electric dipole moment produced by 2 an electron in a static electric field E. The electron experiences a linear restoring force, F = −m!0x, 2 eE = m!0x where !0 characterizes the strength of the atom’s restoring potential. The resulting displacement of charge, eE x = 2 , produces a molecular polarization m!0 pmol = ex eE = 2 m!0 Then, if there are N molecules per unit volume with Z electrons per molecule, the dipole moment per unit volume is P = NZpmol ≡ 0χeE so that NZe2 0χe = 2 m!0 Next, using D = 0E + P E = 0E + 0χeE the relative dielectric constant is = = 1 + χe 0 NZe2 = 1 + 2 m!00 This result changes when there is time dependence to the electric field, with the dielectric constant showing frequency dependence. 1 1.2 Permittivity in the presence of an oscillating electric field Suppose the material is sufficiently diffuse that the applied electric field is about equal to the electric field at each atom, and that the response of the atomic electrons may be modeled as harmonic.
    [Show full text]
  • Magnetic Fields and Forces
    Magnetic Fields and Forces (1) Magnetic Fields are produced by moving charges. (2) Magnetic Fields exert forces on moving charges. (3) Stationary Charges do not produce magnetic fields. (4) Stationary Charges are not affected by stationary magnetic fields. Permanent Magnets There are naturally occurring magnetic substances. These were long used for navigation. As a result, we speak of “north” and “south” magnetic poles, instead of positive and negative magnetic charges. Permanent magnets can also be made by people from raw materials. These magnetic poles also respect an “opposites attract” rule: N S N S attraction N S S N repulsion Earth: North and South Revisited The ancients defined the “north” end of a permanent magnet as the end that is attracted to the “north” pole of the earth. points north S N S Therefore the north geographic pole of earth is a south magnetic pole. N Magnetic Field of a Bar Magnet This is a magnetic dipole field, very similar to the electric dipole field of two opposite electric charges. Note that magnetic field lines are all closed loops, unlike electric field lines that must start and stop on a charge. Important: There is no magnetic “monopole.” N Such a thing has never been observed. North and South magnetic poles always come in pairs of equal strength. Properties of the magnetic force on a charge moving in a B field 1. The magnetic force is proportional to the charge q and speed v of the particle 2. The magnitude and direction of the magnetic force depend on the velocity of the particle and on the magnitude and direction of the magnetic field.
    [Show full text]
  • The Dipole Moment.Doc 1/6
    10/26/2004 The Dipole Moment.doc 1/6 The Dipole Moment Note that the dipole solutions: Qd cosθ V ()r = 2 4πε0 r and Qd 1 =+⎡ θθˆˆ⎤ E ()r2cossin3 ⎣ aar θ ⎦ 4πε0 r provide the fields produced by an electric dipole that is: 1. Centered at the origin. 2. Aligned with the z-axis. Q: Well isn’t that just grand. I suppose these equations are thus completely useless if the dipole is not centered at the origin and/or is not aligned with the z-axis !*!@! A: That is indeed correct! The expressions above are only valid for a dipole centered at the origin and aligned with the z- axis. Jim Stiles The Univ. of Kansas Dept. of EECS 10/26/2004 The Dipole Moment.doc 2/6 To determine the fields produced by a more general case (i.e., arbitrary location and alignment), we first need to define a new quantity p, called the dipole moment: pd= Q Note the dipole moment is a vector quantity, as the d is a vector quantity. Q: But what the heck is vector d ?? A: Vector d is a directed distance that extends from the location of the negative charge, to the location of the positive charge. This directed distance vector d thus describes the distance between the dipole charges (vector magnitude), as well as the orientation of the charges (vector direction). Therefore dd= aˆ , where: Q d ddistance= d between charges d and − Q ˆ ad = the orientation of the dipole Jim Stiles The Univ. of Kansas Dept. of EECS 10/26/2004 The Dipole Moment.doc 3/6 Note if the dipole is aligned with the z-axis, we find that d = daˆz .
    [Show full text]
  • Electromagnetic, Electrostatic and Magnetostatic Fields Electromagnetic Fields Are Characterized by Coupled, Dynamic (Time- Vary
    Electromagnetic, Electrostatic and Magnetostatic Fields Electromagnetic fields are characterized by coupled, dynamic (time- varying) electric and magnetic fields and are governed by the complete set of Maxwell’s equations (four coupled equations). According to Maxwell’s equations, a time-varying electric field cannot exist without the a simultaneous magnetic field, and vice versa. Under static conditions, the time-derivatives in Maxwell’s equations go to zero, and the set of four coupled equations reduce to two uncoupled pairs of equations. One pair of equations governs electrostatic fields while the other set governs magnetostatic fields. This decoupling of Maxwell’s equations illustrates that static electric fields can exist in the absence of magnetic fields and vice versa. Stationary charges produce electrostatic fields while magnetostatic fields are produced by steady (DC) currents or permanent magnets. Maxwell’s Equations (electromagnetic fields) b ` Maxwell’s Equations Maxwell’s Equations (electrostatic fields) (magnetostatic fields) Electrostatic Fields Electrostatic fields are static (time-invariant) electric fields produced by static (stationary) charges. The mathematical definition of the electrostatic field is derived from Coulomb’s law which defines the vector force between two point charges. Coulomb’s Law Given point charges [q1, q2 (units=C)] in air located by vectors R1 and R2, respectively, the vector force acting on charge q2 due to q1 [F12 (units=N)] is defined by Coulomb’s law as where is a unit vector pointing from q1 to q2 and åo is the free-space !12 permittivity [åo = 8.854×10 F/m]. The permittivity of air is approximately equal to that of free space (vacuum).
    [Show full text]
  • (Rees Chapters 2 and 3) Review of E and B the Electric Field E Is a Vector
    ELECTROMAGNETISM SUMMARY (Rees Chapters 2 and 3) Review of E and B The electric field E is a vector function. E q q o If we place a second test charged qo in the electric field of the charge q, the two spheres will repel each other. The strength of the radial force Fr is proportional to the product of the charges and inversely proportional to the distance between them squared. 1 qoq Fr = Coulomb's Law 4πεo r2 -12 where εo is the electric permittivity (8.85 x 10 F/m) . The radial component of the electric field is the force divided by the strength of the test charge qo. 1 q force ML Er = - 4πεo r2 charge T2Q The magnetic field B is also a vector function. Magnetic fields are generated by charges in motion. For example, a current traveling through a wire will produce a magnetic field. A charge moving through a uniform magnetic field will experience a force that is proportional to the component of velocity perpendicular to the magnetic field. The direction of the force is perpendicular to both v and B. X X X X X X X X XB X X X X X X X X X qo X X X vX X X X X X X X X X X F X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X F = qov ⊗ B The particle will move along a curved path that balances the inward-directed force F⊥ and the € outward-directed centrifugal force which, of course, depends on the mass of the particle.
    [Show full text]
  • The Electric Field
    Phys102 Lecture 2 - 1 Phys102 Lecture 2 The Electric Field Key Points • Coulomb’s Law • The electric field (E is a vector!) References Textbook: 16-1,2,3,4,5,6,7,8,9,+. The Electric Field The electric field is defined as the force on a small charge, divided by the magnitude of the charge: The Electric Field An electric field surrounds every charge. The Electric Field For a point charge: The magnitude of the electric field due to charge Q : 1 Q E 2 4 0 r The Electric Field Force on a point charge in an electric field: Example: Electric field above two point charges. Calculate the total electric field (a) at point A and (b) at point B in the figure due to both charges, Q1 and Q2. Example: Electric field above two point charges. Calculate the total electric field (a) at point A and (b) at point B in the figure due to both charges, Q1 and Q2. 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. 4. Check your answer! Field Lines The electric field can be represented by field lines. These lines start on a positive charge and end on a negative charge. 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.
    [Show full text]
  • Chapter 20: Electric Potential and Electric Potential Energy  2
    Chapter 20: Electric Potential and Electric Potential Energy 2. A 4.5 µC charge moves in a uniform electric field Ex=(4.1 × 105 N/C) ˆ . The change in electric potential energy of a charge that moves against an electric field is given by equation 20-1, ∆=U q0 Ed . If the charge moves in the same direction as the field, the work done by the field is positive and ∆=−=−=−U W Fd q0 Ed . If the charge moves in a direction perpendicular to the field, the work and change in potential energy are both zero. The change in potential energy from point A to point B is independent of the path the charge takes between those two points. 1. (a) The charge moves ∆=U 0 perpendicular to the field: 2. (b) The charge moves in the − ∆=−U q Ed =−×4.5 1065 C 4.1 × 10 N/C 6.0m=− 11 J same direction as the field: 0 ( )( )( ) 3. (c) The potential energy changes by an amount ∆=−U 0 11 J =−11 J equal to the sum of paths 1 and 2 above: 9. The vertical electric field of the earth creates a potential difference between two different heights. Because the electric field is uniform, the magnitude potential difference is simply the product of the field and the distance ∆s in the direction of the field (equation 20-4). Solve equation 20-4 for ∆V : ∆V = Es ∆=(100 V/m)( 555 ft× 0.305 m/ft) = 2 × 104 V = 20 kV 11. A potential difference across the gap of a spark plug produces a sufficiently large electric field to produce a spark.
    [Show full text]