Section Summary

Section Summary

2.1 Electric Potential Energy: Potential Difference

  • Electric potential is potential energy per unit charge.
  • The potential difference between points A and B, VBVA,VBVA, size 12{V rSub { size 8{B} } -V rSub { size 8{A} } } {} defined to be the change in potential energy of a charge qq size 12{q} {} moved from A to B, is equal to the change in potential energy divided by the charge, Potential difference is commonly called voltage, represented by the symbol ΔV.ΔV. size 12{V= { {"PE"} over {q} } "." } {}
    ΔV =ΔPEqand ΔPE = qΔVΔV =ΔPEqand ΔPE = qΔV size 12{?V= { {?"PE"} over {q} } " and "D"PE="q?V "." } {}
  • An electron volt is the energy given to a fundamental charge accelerated through a potential difference of 1 V. In equation form
    1 eV=1.60×10–19 C1 V=1.60×10–19C1 J/C=1.60×10–19 J.1 eV=1.60×10–19 C1 V=1.60×10–19C1 J/C=1.60×10–19 J.
  • Mechanical energy is the sum of the kinetic energy and potential energy of a system, that is, KE+PE.KE+PE. size 12{"KE"+"PE"} {} This sum is a constant.

2.2 Electric Potential in a Uniform Electric Field

  • The voltage between points A and B is
    VAB=EdE=VABd(uniformE- field only),VAB=EdE=VABd(uniformE- field only),
    where dd size 12{d} {} is the distance from A to B, or the distance between the plates.
  • In equation form, the general relationship between voltage and electric field is
    E=ΔVΔs,E=ΔVΔs, size 12{E= - { {ΔV} over {Δs} } } {}
    where ΔsΔs size 12{Δs} {} is the distance over which the change in potential, ΔV,ΔV, size 12{Δ`V} {} takes place. The minus sign tells us that EE size 12{E} {} points in the direction of decreasing potential. The electric field is said to be the gradient—as in grade or slope—of the electric potential.

2.3 Electrical Potential Due to a Point Charge

  • Electric potential of a point charge is V=kQ/r.V=kQ/r. size 12{V= ital "kQ"/r} {}
  • Electric potential is a scalar, and electric field is a vector. Addition of voltages as numbers gives the voltage due to a combination of point charges, whereas addition of individual fields as vectors gives the total electric field.

2.4 Equipotential Lines

  • An equipotential line is a line along which the electric potential is constant.
  • An equipotential surface is a three-dimensional version of equipotential lines.
  • Equipotential lines are always perpendicular to electric field lines.
  • The process by which a conductor can be fixed at zero volts by connecting it to Earth with a good conductor is called grounding.

2.5 Capacitors and Dielectrics

  • A capacitor is a device used to store charge.
  • The amount of charge QQ size 12{Q} {} a capacitor can store depends on two major factors—the voltage applied and the capacitor’s physical characteristics, such as its size.
  • The capacitance CC size 12{C} {} is the amount of charge stored per volt, or
    C=QV.C=QV. size 12{C=Q/V} {}
  • The capacitance of a parallel plate capacitor is C=ε0Ad,C=ε0Ad, size 12{C=e rSub { size 8{0} } A/d} {} when the plates are separated by air or free space. ε0ε0 is called the permittivity of free space.
  • A parallel plate capacitor with a dielectric between its plates has a capacitance given by
    C=κε0Ad,C=κε0Ad, size 12{C=e rSub { size 8{0} } A/d} {}
    where κκ is the dielectric constant of the material.
  • The maximum electric field strength above which an insulating material begins to break down and conduct is called dielectric strength.

2.6 Capacitors in Series and Parallel

  • Total capacitance in series 1CS=1C1+1C2+1C3+...1CS=1C1+1C2+1C3+... size 12{ { {1} over { {C} rSub { size 8{S} } } } = { {1} over { {C} rSub { size 8{1} } } } + { {1} over { {C} rSub { size 8{2} } } } + { {1} over { {C} rSub { size 8{3} } } } + "." "." "." } {}
  • Total capacitance in parallel Cp=C1+C2+C3+...Cp=C1+C2+C3+... size 12{ {C} rSub { size 8{p} } = {C} rSub { size 8{1} } + {C} rSub { size 8{2} } + {C} rSub { size 8{3} } + "." "." "." } {}
  • If a circuit contains a combination of capacitors in series and parallel, identify series and parallel parts, compute their capacitances, and then find the total.

2.7 Energy Stored in Capacitors

  • Capacitors are used in a variety of devices, including defibrillators, microelectronics such as calculators, and flash lamps, to supply energy.
  • The energy stored in a capacitor can be expressed in three ways:
    Ecap=QV2=CV22=Q22C,Ecap=QV2=CV22=Q22C, size 12{E rSub { size 8{"cap"} } = { { ital "QV"} over {2} } = { { ital "CV" rSup { size 8{2} } } over {2} } = { {Q rSup { size 8{2} } } over {2C} } } {}
    where QQ size 12{Q} {} is the charge, VV size 12{V} {} is the voltage, and CC size 12{C} {} is the capacitance of the capacitor. The energy is in joules when the charge is in coulombs, voltage is in volts, and capacitance is in farads.