Qausi-static displacement current (Purcell)

Click For Summary
SUMMARY

The discussion centers on the concept of "quasi-static" displacement current as presented in Purcell's "Electricity and Magnetism." Specifically, it addresses the mathematical relationship where the curl of the displacement current density, Jd, is expressed as curl Jd = -(1/4πε)(∂²B/∂t²). This indicates that for slowly varying fields, curl Jd approaches zero, leading to the conclusion that the magnetic field B must also be zero. The participant seeks clarification on the reasoning behind this implication.

PREREQUISITES
  • Understanding of Maxwell's equations
  • Familiarity with electromagnetic theory
  • Knowledge of vector calculus, particularly curl operations
  • Basic concepts of magnetic fields and their behavior in varying electric fields
NEXT STEPS
  • Study Maxwell's equations in detail, focusing on the displacement current term
  • Review vector calculus, specifically the properties and implications of the curl operator
  • Examine the relationship between electric fields and magnetic fields in electromagnetic waves
  • Explore Purcell's "Electricity and Magnetism" for deeper insights into electromagnetic theory
USEFUL FOR

This discussion is beneficial for physics students, educators in electromagnetism, and anyone seeking to deepen their understanding of displacement current and its implications in classical electromagnetism.

shooba
Messages
9
Reaction score
0
"Qausi-static" displacement current (Purcell)

Hello all,
On page 329, chapter 9 of Purcell's E&M book, he describes why the "displacement current" produces nearly zero magnetic field for slowly varying fields. By taking the curl of the displacement current Jd, he shows that curlJd=-(1/4[itex]\pi[/itex]c)(∂2B/∂t2), so that for slowly varying fields, curlJd is nearly zero. From this, using a symmetry/superposition argument he concludes that there can be no magnetic field for such a current distribution. It is this last step that I do not understand; how does curlJd=0 imply B=0?
Thanks!
 
Physics news on Phys.org


Bump? Maybe this belongs in the classical physics section?
 

Similar threads

Graduate Voltage and current waves in a transmission line
  • · Replies 4 ·
Replies
4
Views
3K
Graduate Displacement and conduction currents
  • · Replies 5 ·
Replies
5
Views
2K
Graduate Why is "method of image current" valid in magnetostatics?
  • · Replies 4 ·
Replies
4
Views
2K
Graduate Solving Maxwell's Equations for Electric Field of AC Wire
  • · Replies 11 ·
Replies
11
Views
3K
Graduate Static magnetic field from time-varying electric field
  • · Replies 4 ·
Replies
4
Views
2K
Displacement current and magnetic flux through a wire loop
  • · Replies 1 ·
Replies
1
Views
2K
Undergrad What does Purcell actually say about electromagnetism and relativity?
  • · Replies 32 ·
2
Replies
32
Views
7K
Engineering Current density calculation in anisotropic ferromagnetic film
  • · Replies 7 ·
Replies
7
Views
2K
Line charge creating induced emf and displacement current
  • · Replies 1 ·
Replies
1
Views
2K
Graduate Magnetic Field Computation from Thick Rectangular Conductor
  • · Replies 9 ·
Replies
9
Views
5K