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- https://phys.libretexts.org/Bookshelves/Mathematical_Physics_and_Pedagogy/Mathematical_Methods/The_Multipole_ExpansionA multipole expansion is a mathematical series representing a function that depends on angles—usually the two angles on a sphere. These series are useful because they can often be truncated, meaning t...A multipole expansion is a mathematical series representing a function that depends on angles—usually the two angles on a sphere. These series are useful because they can often be truncated, meaning that only the first few terms need to be retained for a good approximation to the original function. Multipole expansions are very frequently used in the study of electromagnetic and gravitational fields, where the fields at distant points are given in terms of sources in a small region.
- https://phys.libretexts.org/Courses/University_of_California_Davis/UCD%3A_Physics_9C__Electricity_and_Magnetism/1%3A_Electrostatic_Fields/1.4%3A_DipolesParticles we encounter (such as atoms and molecules) rarely are electrically charged, as they tend to attract and bond with other particles that are oppositely-charged. But these neutrally-charged par...Particles we encounter (such as atoms and molecules) rarely are electrically charged, as they tend to attract and bond with other particles that are oppositely-charged. But these neutrally-charged particles are still affected by electric fields, thanks to their component charges being ever-so-slightly separated.
- https://phys.libretexts.org/Bookshelves/University_Physics/Physics_(Boundless)/21%3A_Magnetism/21.6%3A_Applications_of_MagnetismMass spectrometers use electric or magnetic fields to identify different materials.
- https://phys.libretexts.org/Courses/Joliet_Junior_College/PHYS202_-_JJC_-_Testing/01%3A_Conceptual_Objective_1/1.01%3A_OverviewAtoms contain negatively charged electrons and positively charged protons; the number of each determines the atom’s net charge.
- https://phys.libretexts.org/Bookshelves/University_Physics/Physics_(Boundless)/17%3A_Electric_Charge_and_Field/17.1%3A_OverviewAtoms contain negatively charged electrons and positively charged protons; the number of each determines the atom’s net charge.
- https://phys.libretexts.org/Courses/Muhlenberg_College/Physics_122%3A_General_Physics_II_(Collett)/01%3A_Electric_Charges_and_Fields/1.08%3A_Electric_DipolesEarlier we discussed, and calculated, the electric field of a dipole: two equal and opposite charges that are “close” to each other. (In this context, “close” means that the distance d between the two...Earlier we discussed, and calculated, the electric field of a dipole: two equal and opposite charges that are “close” to each other. (In this context, “close” means that the distance d between the two charges is much, much less than the distance of the field point P, the location where you are calculating the field.) Let’s now consider what happens to a dipole when it is placed in an external field.
- https://phys.libretexts.org/Courses/Kettering_University/Electricity_and_Magnetism_with_Applications_to_Amateur_Radio_and_Wireless_Technology/16%3A_Direct_Calculation_of_Electrical_Quantities_from_Charge_Distributions/16.02%3A_Electric_DipolesEarlier we discussed, and calculated, the electric field of a dipole: two equal and opposite charges that are “close” to each other. (In this context, “close” means that the distance d between the two...Earlier we discussed, and calculated, the electric field of a dipole: two equal and opposite charges that are “close” to each other. (In this context, “close” means that the distance d between the two charges is much, much less than the distance of the field point P, the location where you are calculating the field.) Let’s now consider what happens to a dipole when it is placed in an external field.
- https://phys.libretexts.org/Workbench/NATSCI-1A/PHYSC-11_Text_(FCC)/15%3A_Atomic_Theory_and_Periodic_Table/15.10%3A_Molecular_Structure_and_PolarityVSEPR theory predicts the three-dimensional arrangement of atoms in a molecule. It states that valence electrons will assume an electron-pair geometry that minimizes repulsions between areas of high e...VSEPR theory predicts the three-dimensional arrangement of atoms in a molecule. It states that valence electrons will assume an electron-pair geometry that minimizes repulsions between areas of high electron density (bonds and/or lone pairs). Molecular structure, which refers only to the placement of atoms in a molecule and not the electrons, is equivalent to electron-pair geometry only when there are no lone electron pairs around the central atom.
- https://phys.libretexts.org/Courses/Joliet_Junior_College/PHYS202_-_JJC_-_Testing/04%3A_Chapter_4/4.01%3A_Electric_DipolesEarlier we discussed, and calculated, the electric field of a dipole: two equal and opposite charges that are “close” to each other. (In this context, “close” means that the distance d between the two...Earlier we discussed, and calculated, the electric field of a dipole: two equal and opposite charges that are “close” to each other. (In this context, “close” means that the distance d between the two charges is much, much less than the distance of the field point P, the location where you are calculating the field.) Let’s now consider what happens to a dipole when it is placed in an external field.
- https://phys.libretexts.org/Bookshelves/University_Physics/Physics_(Boundless)/18%3A_Electric_Potential_and_Electric_Field/18.1%3A_OverviewElectric potential and field are related in that potential is a property of the field that describes the field’s action.
- https://phys.libretexts.org/Bookshelves/Electricity_and_Magnetism/Electricity_and_Magnetism_(Tatum)/03%3A_Dipole_and_Quadrupole_Moments/3.07%3A_The_Simple_DipoleAs you may expect from the title of this section, this will be the most difficult and complicated section of this chapter so far. Our aim will be to calculate the field and potential surrounding a sim...As you may expect from the title of this section, this will be the most difficult and complicated section of this chapter so far. Our aim will be to calculate the field and potential surrounding a simple dipole.
