Electric Field Confusion: Explaining E=-∇V & E=-∇V-∂A/∂t

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SUMMARY

The discussion clarifies the equations for electric fields: E=-∇V applies to electrostatics, where the electric field is conservative and its curl is zero, while E=-∇V-∂A/∂t is relevant in electrodynamics, accounting for time-varying electric and magnetic fields. The distinction between these two scenarios is crucial for understanding electromagnetic theory. Participants emphasize the importance of foundational knowledge in electromagnetism (EM) to grasp these concepts fully.

PREREQUISITES
  • Understanding of vector calculus, specifically gradient and curl operations.
  • Familiarity with electrostatics and the concept of conservative fields.
  • Basic knowledge of electrodynamics and Maxwell's equations.
  • Experience with electromagnetic theory, particularly the relationship between electric and magnetic fields.
NEXT STEPS
  • Study the principles of vector calculus, focusing on gradient and curl.
  • Learn about electrostatics and conservative fields in detail.
  • Explore Maxwell's equations and their implications in electrodynamics.
  • Investigate the role of time-varying fields in electromagnetic theory.
USEFUL FOR

Students of physics, particularly those studying electromagnetism, educators teaching electromagnetic theory, and professionals working in fields related to electrical engineering and physics research.

Isaac0427
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Hi all! I know that this might be a stupid question, but I am very confused about a particular aspect of the electric field. I have seen these equations:
E=-∇V and E=-∇V-∂A/∂t
Could you guys explain how the electric field can be explained with or without -∂A/∂t
 
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The first is for electrostatic case where the electric field is a conservative field (its curl vanishes), the second is in the case of electrodynamics where both electric and magnetic fields are changing with time. Have you taken EM course?
 
blue_leaf77 said:
The first is for electrostatic case where the electric field is a conservative field (its curl vanishes), the second is in the case of electrodynamics where both electric and magnetic fields are changing with time. Have you taken EM course?
Thanks, and no I havent.
 

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