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7.1 Electric Potential Energy

  • The work done to move a charge from point A to B in an electric field is path independent, and the work around a closed path is zero. Therefore, the electric field and electric force are conservative.
  • We can define an electric potential energy, which between point charges is U(r)=keqQrU(r)=keqQr, with the zero reference taken to be at infinity.
  • The superposition principle holds for electric potential energy; the potential energy of a system of multiple charges is the sum of the potential energies of the individual pairs.

7.2 Electric Potential and Potential Difference

  • Electric potential is potential energy per unit charge.
  • The potential difference between points A and B, VBVA,VBVA, that is, the change in potential of a charge 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 ΔVΔV:
  • An electron-volt is the energy given to a fundamental charge accelerated through a potential difference of 1 V. In equation form,
    =(1.60×10−19C)(1J/C)=1.60×10−19J. =(1.60×10−19C)(1J/C)=1.60×10−19J.

7.3 Calculations of Electric Potential

  • Electric potential is a scalar whereas electric field is a vector.
  • Addition of voltages as numbers gives the voltage due to a combination of point charges, allowing us to use the principle of superposition: VP=ke1NqiriVP=ke1Nqiri.
  • An electric dipole consists of two equal and opposite charges a fixed distance apart, with a dipole moment p=qdp=qd.
  • Continuous charge distributions may be calculated with VP=kedqrVP=kedqr.

7.4 Determining Field from Potential

  • Just as we may integrate over the electric field to calculate the potential, we may take the derivative of the potential to calculate the electric field.
  • This may be done for individual components of the electric field, or we may calculate the entire electric field vector with the gradient operator.

7.5 Equipotential Surfaces and Conductors

  • An equipotential surface is the collection of points in space that are all at the same potential. Equipotential lines are the two-dimensional representation of equipotential surfaces.
  • Equipotential surfaces are always perpendicular to electric field lines.
  • Conductors in static equilibrium are equipotential surfaces.
  • Topographic maps may be thought of as showing gravitational equipotential lines.

7.6 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.
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