Curl of an electric dipole field

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SUMMARY

The discussion centers on the nature of the electric dipole field and its conservativeness. It is established that the curl of the gradient of a scalar function is zero, indicating that electric fields derived from scalar potentials are conservative. However, the behavior of a positively charged rod in an electric dipole field, which can rotate, suggests that one must consider both rotational and translational energy when applying the conservation of energy principle. The conclusion drawn is that while the electric dipole field can exhibit non-conservative characteristics due to rotational dynamics, it does not negate the fundamental properties of conservative fields.

PREREQUISITES
  • Vector calculus fundamentals
  • Understanding of electric dipole and monopole fields
  • Knowledge of conservative and non-conservative forces
  • Familiarity with energy conservation principles
NEXT STEPS
  • Study the properties of electric dipole fields in detail
  • Learn about the mathematical formulation of curl in vector calculus
  • Explore the implications of rotational dynamics in electric fields
  • Investigate the differences between conservative and non-conservative forces in physics
USEFUL FOR

This discussion is beneficial for physics students, educators, and professionals interested in electromagnetism, particularly those exploring the characteristics of electric fields and energy conservation principles.

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Is the field of an electric dipole conservative?

Initially I thought it would be, for no particular reason but that's just what my high school intuition thought. (haha I thought everything would be conservative apart from friction)

But I was reading up on some vector calculus and discovered

\mbox{curl}(\nabla f) = \mathbf{0}

If you put a positively charged rod in an electric dipole field, and fix it at the right orientation, it will rotate. Does that mean that the field is not conservative?


EDIT: I just realized it would also rotate in an electric monopole field lol

thanks
 
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It just means you have to include rotational as well as translational energy in applying conservation of energy.
 

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