Help with curls and current density 1

In summary, the problem involves obtaining H from a given current density in cylindrical coordinates and then comparing the curl of H with J. The solution involves taking the integral of the inverse of the del operator and using the aphi component of the curl operator to yield the same component of J.
  • #1
FatoonsBaby71
14
0
Help with curls and current density!1

Homework Statement


In cylindrical coordinates, J = 105*(cos(2r)2)*az in a certain region. Obtain H from this current density and then take the curl of H and compare with J.

Answer H = 105*(r/4+sin4r/8+cos4r/32r-1/32r)aphi


Homework Equations


J = Del Operator X H


The Attempt at a Solution


Well I know I will be working backwards here. I am given the current density and they want H. However can anyone provide hints for me for the inverse of the del operator. Am I just going ot take the integral of everything as opposed to the partial derivative.??

Thanks
 
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  • #2


FatoonsBaby71 said:

Homework Statement


In cylindrical coordinates, J = 105*(cos(2r)2)*az in a certain region. Obtain H from this current density and then take the curl of H and compare with J.

Answer H = 105*(r/4+sin4r/8+cos4r/32r-1/32r)aphi


Homework Equations


J = Del Operator X H


The Attempt at a Solution


Well I know I will be working backwards here. I am given the current density and they want H. However can anyone provide hints for me for the inverse of the del operator. Am I just going ot take the integral of everything as opposed to the partial derivative.??

Thanks
Here the current density has only one component (az). Which component of the curl operator will yield this components of J?
 
  • #3


Telling from the answer it looks like aphi
 
  • #4


FatoonsBaby71 said:
Telling from the answer it looks like aphi
I meant in terms of partial differentials.
 

1. What is the relationship between current density and curls?

The current density is a vector quantity that describes the amount of electric current flowing through a material per unit area. Curls, on the other hand, represent the local rotation or circulation of the electric field. The relationship between current density and curls is described by the Maxwell's equations, which state that the curl of the magnetic field is directly proportional to the current density.

2. How does current density affect the strength of an electric field?

Current density plays a crucial role in determining the strength of an electric field. The higher the current density, the stronger the electric field will be. This is because a larger amount of electric current flowing through a smaller area will result in a higher concentration of electric charge and, consequently, a stronger electric field.

3. What factors influence the magnitude of current density?

The magnitude of current density is influenced by several factors, including the type of material, the cross-sectional area, and the applied voltage. Materials with a higher conductivity will have a larger current density for the same amount of applied voltage. Similarly, increasing the cross-sectional area of a material will decrease the current density, while increasing the applied voltage will increase the current density.

4. How does current density affect the heating of a material?

Current density plays a significant role in determining the amount of heat generated in a material. As the current density increases, the number of collisions between charged particles and atoms in the material also increases, resulting in a higher rate of energy transfer and, consequently, more heat production. This is the principle behind the heating of conductors in electrical circuits.

5. What are some practical applications of understanding current density and curls?

Understanding the relationship between current density and curls is essential for various practical applications in electrical engineering. It is used to analyze and design electric circuits, calculate the strength of magnetic fields in devices such as motors and generators, and determine the heating effects of current on materials. Additionally, understanding current density and curls is crucial in the development of technologies such as wireless power transfer and electromagnetic imaging techniques.

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