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Interaction of Charged Objects

Interaction of Charged Objects. Repulsion: can happen only for like-charged objects!. Attraction: can happen also for like-charged objects!. Intervening matter does not “ block ” the E field. The resulting field is a superposition of two fields :

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Interaction of Charged Objects

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  1. Interaction of Charged Objects Repulsion: can happen only for like-charged objects! Attraction: can happen also for like-charged objects! Intervening matter does not“block” the E field The resulting field is a superpositionof two fields: Field of the charge plus the field of induced dipoles. - + +

  2. Clicker Question A B D C What is the direction of the electric field at X due to the dipole?

  3. Clicker Question A B D C What is the direction of the electric field at X due to the plastic block?

  4. Clicker Question A B D C What is the direction of the NET electric field at X?

  5. Clicker Question • The force of one of the permanent dipoles on the other is: • Attractive • Repulsive • The force is zero

  6. Conductors and Insulators Different materials respond differently to electric field Conductor: contains mobile charges that can move through material Insulator: contains no mobile charges

  7. Polarization of Insulators Insulator: Electrons are bound to the atoms or molecules. Electrons can shift slightly (<1 Å), but remain bound to the molecule. Individual atoms or molecules can be polarized by external electric field. There are a lot of molecules – the net effect produced by the induced dipoles can be very large.

  8. Polarization of Insulators Diagram showing polarization of an insulator: Dipoles: exaggerated in size; stretch: degree of polarization No mobile charges: excess charges stay where they are

  9. Low Density Approximation Field E at a location of a molecule is a superposition of the external applied field and the field created by other induced dipoles: Simplifying assumption:

  10. Conductors There are charges which can move freely throughout the material E In contrast to an insulator, where electrons and nuclei can move only very small distances, the charged particles in a conductor are free to move large distances. Polarization of conductors differs from that of insulators.

  11. Ionic Solutions are Conductors Salt water: Na+ and Cl- H+ and OH- Apply external electric field When an electric field is applied to a conductor, the mobile charged particles begin to move in the direction of the force exerted on them by the field. As the charges move, they begin to pile up in one location, creating a concentration of charge  creates electric field. The net electric field is the superposition of the applied field and field created by the relocated charges.

  12. Ionic Solutions are Conductors Assumption:charges will move until Enet=0 (static equilibrium) Proof: by contradiction: Assume Enet≠0 Mobile ions will move This is not equilibrium Assumption Enet≠0 is wrong Enet=0 It is not a shielding effect, but a consequence of superposition!

  13. A Model of a Metal Positive atomic cores and mobile-electron sea Metal lattice Electrons are not completely free – they are bound to the metal as a whole. We will return to this idea when we discuss the force on a current carrying wire in a magnetic field. There is no net interaction between mobile electrons

  14. Metal in Electric Field Note:It is not charged! Net charge is still zero Simplified diagram of polarized metal

  15. Electric Field inside Metal In static equilibrium: Enet= 0 everywhere inside the metal! Mobile charges on surface rearrange to achieve Enet= 0 Actual arrangement might be very complex! It is a consequence of 1/r2 distance dependence Enet= 0 only in static equilibrium!

  16. Drude Model of Electron Motion in a Metal - • No net interaction between mobile electrons • Forget previous velocity after collision conductivity ()  μ Collisions: - impurities - thermal motion of atoms Higher temperature T  shorter  lower

  17. Excess Charge on Conductors Excess charges in any conductor are always found on an inner or outer surface!

  18. Conductors versus Insulators

  19. Charging and Discharging Discharging by contact: On approach: body polarizes On contact: charge redistributes over larger surface Grounding: connection to earth (ground) – very large object

  20. Charging by Induction

  21. Charging by Induction

  22. Exercise An object can be both charged and polarized + On a negatively charged metal ball excess charge is spread uniformly all over the surface. What happens if a positive charge is brought near?

  23. When the Field Concept is less Useful +q Splitting universe into two parts does not always work. If q is so small that it does not appreciably alter the charge distribution on the sphere, then we can still use the original field: Otherwise, we must calculate new field:

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