What is the curl of a electric field?

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SUMMARY

The curl of an electric field is zero in the context of electrostatics, represented mathematically as \(\vec { \nabla } \times \vec { E } = 0\). This is applicable when dealing with stationary charges, where no magnetic field exists, leading to \(\frac{\partial \vec {B}}{\partial t} = 0\). However, according to Maxwell's third equation, the curl of an electric field is equal to the negative time derivative of the magnetic field, \(\vec { \nabla } \times \vec { E } = -\frac{\partial}{\partial t} \vec {B}\). The confusion arises when considering dynamic situations where the magnetic field changes over time.

PREREQUISITES
  • Understanding of Maxwell's equations
  • Knowledge of vector calculus
  • Familiarity with electrostatics and magnetic fields
  • Basic physics concepts related to electric and magnetic fields
NEXT STEPS
  • Study Maxwell's equations in detail, focusing on the implications of the curl operator
  • Learn about the relationship between electric fields and magnetic fields in dynamic systems
  • Explore the concept of electromagnetic induction and its mathematical representation
  • Investigate the conditions under which the curl of an electric field is non-zero
USEFUL FOR

Physics students, electrical engineers, and anyone studying electromagnetism will benefit from this discussion, particularly those seeking clarity on the behavior of electric fields in static and dynamic contexts.

back2square1
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This should be simple but I know I'm going wrong somewhere and I can't figure out where.
The curl of a electric field is zero,
i.e. \vec { \nabla } \times \vec { E } = 0
Because , no set of charge, regardless of their size and position could ever produce a field whose curl is not zero.

But,
Maxwell's 3rd Equation tells us that,
the curl of a electric field is equal to the negative partial time derivative of magnetic field \vec {B}.
i.e. \vec { \nabla } \times \vec { E } = -\frac { \partial }{ \partial t } \vec { B }

So is the curl zero or is it not? If we equate those two equations we get that the time derivative of magnetic field is zero. What's wrong? What am I missing?
 
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back2square1 said:
The curl of a electric field is zero,
i.e. \vec { \nabla } \times \vec { E } = 0

That should read, "the curl of an electrostatic field is zero," that is, the electric field associated with a set of stationary charges has a curl of zero. In this situation, there is no magnetic field, so ##\partial \vec B / \partial t = 0##.
 
Oh. Thanks. Got it. Sometimes things as simple as this slip off.
 

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