Curl Calculator

Curl Calculator

Curl calculator is used to find the curl of a vector function at the given points of the function x, y, and z. 

What is the curl of a vector?

A vector field can be rotated using the vector operation called curl. It is symbolized by the letter F, where F stands for the vector field. A vector field that represents the rotation of the initial vector field is the outcome of the curl operation.

Formula

The curl formula is shown below,

• “∇” This sign is called Nabla.
• A (A_x, A_y, A_z) is the function

Properties of Curl:

The curl of a vector field has the following properties:

• The curl is a vector field.
• A vector field's curl indicates the degree of rotation.
• if a vector field has zero curls, it means that the field is conservative.

Applications of Curl:

The curl of a vector field has numerous applications in physics and engineering. Here are a few most common applications:

Fluid Dynamics:

The rotation of the fluid is described in fluid dynamics by the curl of the velocity field. It is a crucial parameter in the investigation of vortices.

Electromagnetism:

In electromagnetism, the curl of the electric field is used to calculate the magnetic field, and the curl of the magnetic field is used to calculate the electric field. The curl of a vector field is invariant under translation and rotation.

How to evaluate the curl?

 Example

Find the curl of the given function F = (3x²y + 5xy² + 4z) with the given points (5, 7, 6)

Solution:

The given function is three-dimensional so, in the first step we write the determinant of three functions according to the definition,

Step 1: The determinant is

curl = ∇ × F

= c[(∂ / ∂y (4z) - ∂ / ∂z (5xy²)), ∂ / ∂z (3x²y) - ∂ / ∂x (4z), ∂ / ∂x (5xy²) - ∂ / ∂y (3x²y)]

Step 2: Find the partial derivative

∂ / ∂y (4z) = 0

∂ / ∂y (3x²y) = 0

∂ / ∂x (4z) = 0

∂ / ∂x (5xy²) = 0

∂ / ∂z (5xy²) = 5y²

∂ / ∂z (3x²y) = 3x²

Step 3: Now put the partial derivative and get the curl,

curl(3x²y + 5xy² + 4z) = (0, 0, -3x² + 5y²)

Step 4: Put the given point in x, y, and z the result is

curl(3x²y + 5xy² + 4z)_{(5, 7, 6)} = (0, 0, 170)