Section Summary

Section Summary

1.1 Static Electricity and Charge: Conservation of Charge

  • There are only two types of charge, which we call positive and negative.
  • Like charges repel, unlike charges attract, and the force between charges decreases with the square of the distance.
  • The vast majority of positive charge in nature is carried by protons, while the vast majority of negative charge is carried by electrons.
  • The electric charge of one electron is equal in magnitude and opposite in sign to the charge of one proton.
  • An ion is an atom or molecule that has nonzero total charge due to having unequal numbers of electrons and protons.
  • The SI unit for charge is the coulomb (C), with protons and electrons having charges of opposite sign but equal magnitude; the magnitude of this basic charge q e q e size 12{ lline q rSub { size 8{e} } rline} {} is
    q e = 1.60 × 10 19 C . q e = 1.60 × 10 19 C . size 12{ lline q rSub { size 8{e} } rline =1 "." "60" times "10" rSup { size 8{ - "19"} } C} {}
  • Whenever charge is created or destroyed, equal amounts of positive and negative are involved.
  • Most often, existing charges are separated from neutral objects to obtain some net charge.
  • Both positive and negative charges exist in neutral objects and can be separated by rubbing one object with another. For macroscopic objects, negatively charged means an excess of electrons and positively charged means a depletion of electrons.
  • The law of conservation of charge ensures that whenever a charge is created, an equal charge of the opposite sign is created at the same time.

1.2 Conductors and Insulators

  • Polarization is the separation of positive and negative charges in a neutral object.
  • A conductor is a substance that allows charge to flow freely through its atomic structure.
  • An insulator holds charge within its atomic structure.
  • Objects with like charges repel each other, while those with unlike charges attract each other.
  • A conducting object is said to be grounded if it is connected to Earth through a conductor. Grounding allows transfer of charge to and from Earth's large reservoir.
  • Objects can be charged by contact with another charged object and obtain the same sign charge.
  • If an object is temporarily grounded, it can be charged by induction, and obtains the opposite sign charge.
  • Polarized objects have their positive and negative charges concentrated in different areas, giving them a nonsymmetrical charge.
  • Polar molecules have an inherent separation of charge.

1.3 Coulomb's Law

  • Frenchman Charles Coulomb was the first to publish the mathematical equation that describes the electrostatic force between two objects.
  • Coulomb's law gives the magnitude of the force between point charges. It is
    F=k|q1q2|r2,F=k|q1q2|r2, size 12{F=k { {q rSub { size 8{1} } q rSub { size 8{2} } } over {r rSup { size 8{2} } } } } {}

    where q1q1 and q2q2 are two point charges separated by a distance r,r, and k8.99×109 N·m2/C2.k8.99×109 N·m2/C2.

  • This Coulomb force is extremely basic, since most charges are due to point-like particles. It is responsible for all electrostatic effects and underlies most macroscopic forces.
  • The Coulomb force is extraordinarily strong compared with the gravitational force, another basic force—but unlike gravitational force it can cancel, since it can be either attractive or repulsive.
  • The electrostatic force between two subatomic particles is far greater than the gravitational force between the same two particles.

1.4 Electric Field: Concept of a Field Revisited

  • The electrostatic force field surrounding a charged object extends out into space in all directions.
  • The electrostatic force exerted by a point charge on a test charge at a distance rr size 12{r} {} depends on the charge of both charges, as well as the distance between the two.
  • The electric field EE size 12{E} {} is defined to be
    E = F q , E = F q , size 12{E= { {F} over {q,} } } {}

    where FF size 12{F} {} is the Coulomb or electrostatic force exerted on a small positive test charge q.q. size 12{q} {} EE size 12{E} {} has units of N/C.

  • The magnitude of the electric field EE size 12{E} {} created by a point charge QQ size 12{Q} {} is
    E = k |Q| r 2 . E = k |Q| r 2 . size 12{E=k { {Q} over {r rSup { size 8{2} } } } } {}

    where rr size 12{r} {} is the distance from Q.Q. size 12{Q} {} The electric field EE size 12{E} {} is a vector and fields due to multiple charges add like vectors.

1.5 Electric Field Lines: Multiple Charges

  • Drawings of electric field lines are useful visual tools. The properties of electric field lines for any charge distribution are that
  • field lines must begin on positive charges and terminate on negative charges, or at infinity in the hypothetical case of isolated charges,
  • the number of field lines leaving a positive charge or entering a negative charge is proportional to the magnitude of the charge,
  • the strength of the field is proportional to the closeness of the field lines—more precisely, it is proportional to the number of lines per unit area perpendicular to the lines,
  • the direction of the electric field is tangent to the field line at any point in space, and
  • field lines can never cross.

1.6 Conductors and Electric Fields in Static Equilibrium

  • A conductor allows free charges to move about within it.
  • The electrical forces around a conductor will cause free charges to move around inside the conductor until static equilibrium is reached.
  • Any excess charge will collect along the surface of a conductor.
  • Conductors with sharp corners or points will collect more charge at those points.
  • A lightning rod is a conductor with sharply pointed ends that collect excess charge on the building caused by an electrical storm and allow it to dissipate back into the air.
  • Electrical storms result when the electrical field of Earth's surface in certain locations becomes more strongly charged, due to changes in the insulating effect of the air.
  • A Faraday cage acts like a shield around an object, preventing electric charge from penetrating inside.

1.7 Applications of Electrostatics

  • Electrostatics is the study of electric fields in static equilibrium.
  • In addition to research using equipment such as a Van de Graaff generator, many practical applications of electrostatics exist, including photocopiers, laser printers, ink-jet printers, and electrostatic air filters.