Understanding the Curl of a Vector Potential in Spherical Coordinates

In summary, the conversation is about finding the curl of a vector function in spherical coordinates. The student is having trouble finding a good example online and is looking for recommendations for resources. They also mention that they know how the curl is set up in spherical coordinates from their textbook. Eventually, they are able to find the answer thanks to a link provided by another person.
  • #1
saybrook1
101
4

Homework Statement


For some reason I can't find anywhere online that gives a good example of the curl of a vector function in spherical coordinates. I need to compute ∇ X A where

A = [itex]\frac{ksinθ}{r^{2}}[/itex][itex]\widehat{ϕ}[/itex]

If anyone can point me in the right direction of a good video or text tutorial that shows the curl of a vector potential in spherical coordinates I would really appreciate it. Thanks.


Homework Equations



I know how the curl is set up in spherical coordinates from my textbook I'm just not one hundred percent sure how to go about it.

The Attempt at a Solution

 
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  • #3
Just figured it out, thanks a ton!
 

1. What is the concept of "Curl of the vector potential"?

The "Curl of the vector potential" is a mathematical concept used in vector calculus to describe the rotation or circulation of a vector field. It is represented by the symbol ∇ x A, where ∇ is the nabla operator and A is the vector potential.

2. How is the "Curl of the vector potential" calculated?

The "Curl of the vector potential" can be calculated by taking the cross product of the nabla operator and the vector potential. This results in a new vector that represents the magnitude and direction of the rotation or circulation of the original vector field.

3. What is the physical significance of the "Curl of the vector potential"?

The "Curl of the vector potential" has physical significance in electromagnetism, as it is a key component in the equations that describe the behavior of electric and magnetic fields. It helps to determine the strength and direction of these fields at a given point in space.

4. What are some applications of the "Curl of the vector potential"?

The "Curl of the vector potential" has various applications in physics and engineering, including in the study of electromagnetic fields, fluid dynamics, and quantum mechanics. It is also used in the development of computer graphics and simulations.

5. How does the "Curl of the vector potential" relate to other vector calculus concepts?

The "Curl of the vector potential" is closely related to the gradient, divergence, and Laplacian operators, which are all fundamental concepts in vector calculus. It also has connections to other physical principles, such as the conservation of energy and momentum.

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