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Electric Dipole and Equipotential Surfaces

Electric Dipole and Equipotential Surfaces. - Electric dipole Electric field lines Equipotential surfaces. The Electric Potential of a Dipole. z. P. +q. y. -q. x. Find : Potential V at point P anywhere. . Solution. Things to note.

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Electric Dipole and Equipotential Surfaces

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  1. Electric Dipole and Equipotential Surfaces • - Electric dipole • Electric field lines • Equipotential surfaces

  2. The Electric Potential of a Dipole z P +q y -q x Find: Potential V at point P anywhere.

  3. Solution

  4. Things to note The potential for a point charge (monopole) varies as 1/r and the electric field as 1/r2The potential for two charges (dipole) varies as 1/r2 and the electric field as 1/r3 (see Assignment 3) For higher order multi-poles, the potentials will vary as: 1/r3, 1/r4, 1/r5…and the corresponding electric fields at: 1/r4, 1/r5, 1/r6…

  5. Fields and Equipotential Lines/Surfaces(extra) Q: How can we obtain the lines that describe a field, or the equipotential lines associated with it?A: we need one or the other to start with, and use some algebra/calculus.

  6. Example For the field intensity E=Exi + Eyj, how would the flux lines look like?How would the equipotential lines look like?- at any point, dy/dx = Ey/Ex for the field (flux lines)- at any point, the equipotentials are perpendicular, hence they must have a slope: dy/dx = -1/(slope of flux lines)

  7. Example For the field intensity E=y i + x j, how would the flux lines look like?What about the equipotential lines?

  8. Solution

  9. In General, for 3D in any coords:

  10. E and V for a Dipole • The equipotential lines are the dashed blue lines • The electric field lines are the brown lines • The equipotential lines are everywhere perpendicular to the field lines • These lines are a cross section of surfaces !

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