How Does the Curl of Current Density Derive This Expression?

  • Context: Graduate 
  • Thread starter Thread starter TheCanadian
  • Start date Start date
  • Tags Tags
    Curl Derivation Vector
Click For Summary
SUMMARY

The discussion centers on the derivation of an expression related to the curl of current density (J) in electromagnetic theory. The user seeks clarification on how taking the curl of J leads to a specific equation used in a proof. The reference provided points to the Biot-Savart Law, specifically pages 12 and 13, which detail the mathematical framework necessary for understanding this derivation. The conversation emphasizes the importance of grasping vector calculus concepts in the context of electromagnetism.

PREREQUISITES
  • Vector calculus, specifically the operation of curl
  • Electromagnetic theory, particularly the Biot-Savart Law
  • Understanding of current density (J) in physics
  • Mathematical proofs in physics
NEXT STEPS
  • Study the Biot-Savart Law in detail, focusing on its mathematical implications
  • Learn about the properties and applications of the curl operator in vector calculus
  • Explore electromagnetic field theory, particularly the relationship between current density and magnetic fields
  • Review mathematical proofs involving vector fields and their physical interpretations
USEFUL FOR

Students and professionals in physics, particularly those studying electromagnetism, as well as educators seeking to clarify the mathematical foundations of current density and its applications in electromagnetic theory.

TheCanadian
Messages
361
Reaction score
13
I have attached the equation that I do not quite understand how is true. This is the current density and was simply used as a part of a proof. But how is this equation true? How does taking the curl of J give you this expression?
 

Attachments

  • Screen Shot 2016-01-31 at 1.48.08 AM.png
    Screen Shot 2016-01-31 at 1.48.08 AM.png
    2.9 KB · Views: 635
Physics news on Phys.org

Similar threads

Undergrad Curl operator for time-varying vector
  • · Replies 1 ·
Replies
1
Views
2K
High School What Does "Curl" Mean in Vector Fields?
  • · Replies 3 ·
Replies
3
Views
2K
Graduate How to take the spatial derivative of quaternions
  • · Replies 8 ·
Replies
8
Views
3K
Undergrad Ampere's Law For Static Magnetic Field
  • · Replies 5 ·
Replies
5
Views
2K
Undergrad Solve Vector Equation: iy + jx & (i + j)/√2
  • · Replies 3 ·
Replies
3
Views
3K
Undergrad Intuitively understand the curl formula?
  • · Replies 10 ·
Replies
10
Views
3K
Undergrad What do Stokes' and Green's theorems represent?
  • · Replies 7 ·
Replies
7
Views
2K
Undergrad Vector field and Helmholtz Theorem
  • · Replies 20 ·
Replies
20
Views
4K
How to observe if a vector field has curl or not?
  • · Replies 2 ·
Replies
2
Views
4K
Undergrad A math confusion in deriving the curl of magnetic field from Biot-Savart
  • · Replies 0 ·
Replies
0
Views
2K