Why must be that for curl vector in spherical coordinate?

Thread starter Outrageous
Start date Jul 16, 2013
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Coordinate Curl Spherical Vector

In summary, the curl vector in spherical coordinate system is necessary for understanding and analyzing vector fields in three dimensions. It is different from the curl vector in cartesian coordinate due to the use of different coordinate systems and basis vectors. In spherical coordinates, it is calculated using a formula that takes into account the curvature of the coordinate system. The curl vector can be visualized using vector field plots, animations, and 3D models. Its practical applications include fluid mechanics, electromagnetism, celestial mechanics, and computer graphics.

Jul 16, 2013

Outrageous

The correct one is 2nd, but why not first?
Please guide , or tell me any link that relate to this derivation. Thanks

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Jul 16, 2013

SteamKing

Staff Emeritus

Science Advisor

Homework Helper

I'm sorry, but your post is lacking some details.

Jul 16, 2013

Outrageous

I know the second ( divided by r^2sinθ, we will get unit vector also). Why the first one is wrong?
Thanks

Related to Why must be that for curl vector in spherical coordinate?

1. Why is the curl vector in spherical coordinate system necessary?

The curl vector in spherical coordinate system is necessary because it allows us to understand and analyze vector fields in three dimensions. It helps us to determine the rotational behavior of a vector field at any given point, which is crucial in many physical and engineering applications.

2. What is the difference between curl vector in spherical coordinate and cartesian coordinate?

The main difference between curl vector in spherical coordinate and cartesian coordinate is the coordinate system used. In spherical coordinates, the position of a point is described using the radial distance, polar angle, and azimuthal angle, while in cartesian coordinates, it is described using the x, y, and z coordinates. The curl vector is also expressed differently in the two coordinate systems due to their different basis vectors.

3. How is the curl vector calculated in spherical coordinate?

In spherical coordinates, the curl vector is calculated using a formula that involves the partial derivatives of the vector field with respect to the three coordinates (r, θ, and φ). This formula takes into account the curvature of the coordinate system and the non-constant basis vectors. The resulting vector has components in the r, θ, and φ directions.

4. Can the curl vector in spherical coordinate be visualized?

Yes, the curl vector in spherical coordinate can be visualized using vector fields plots. These plots show the direction and magnitude of the curl vector at different points in the coordinate system. It can also be visualized using animations or 3D models to demonstrate the rotational behavior of the vector field.

5. What are some practical applications of the curl vector in spherical coordinate?

The curl vector in spherical coordinate has many practical applications in physics, engineering, and mathematics. It is used in fluid mechanics to study the flow of fluids, in electromagnetism to understand magnetic fields, and in celestial mechanics to analyze the motion of objects in space. It is also used in computer graphics to create realistic 3D models and animations.