Qausi-static displacement current (Purcell)

In summary, Purcell explains that the "displacement current" produces a negligible magnetic field for slowly varying fields. This is because the curl of the displacement current, represented as Jd, is equal to -(1/4\pic)(∂2B/∂t2). Therefore, for slowly varying fields, the curl of Jd is almost zero. Purcell uses a symmetry/superposition argument to conclude that there can be no magnetic field for this type of current distribution, although the last step of how curlJd=0 implies B=0 is not fully understood.
  • #1
shooba
9
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"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!
 
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  • #2


Bump? Maybe this belongs in the classical physics section?
 

What is quasi-static displacement current?

Quasi-static displacement current, also known as Purcell current, is a phenomenon that occurs in a material when an electric field is changing over time. It is a displacement of charges within the material that creates a magnetic field, similar to the way in which a current in a wire creates a magnetic field.

How is quasi-static displacement current related to Maxwell's equations?

Purcell current is a modification of one of Maxwell's equations, specifically the Ampere-Maxwell equation. It was added to the equation to account for the displacement of charges in a changing electric field, which was not accounted for in the original equation.

What are the applications of quasi-static displacement current?

Quasi-static displacement current has various applications in electronics, such as in capacitors, antennas, and transmission lines. It is also important in the study of electromagnetic waves, as it helps to explain the behavior of these waves in different materials.

How is quasi-static displacement current different from conduction current?

Quasi-static displacement current is a displacement of charges within a material, while conduction current is the flow of charges through a material. Quasi-static displacement current only occurs when there is a changing electric field, while conduction current can occur even in a static electric field.

What factors affect the magnitude of quasi-static displacement current?

The magnitude of quasi-static displacement current depends on the rate of change of the electric field, the permittivity of the material, and the size and shape of the material. It also varies with the frequency of the electric field and the conductivity of the material.

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