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# Curl Calculator

Enter functions and points to the required fields and hit the calculate button to use this 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 = (3x^{2}y + 5xy^{2} + 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 (5xy^{2})), ∂ / ∂z (3x^{2}y) - ∂ / ∂x (4z), ∂ / ∂x (5xy^{2}) - ∂ / ∂y (3x^{2}y)]

**Step 2: **Find the partial derivative

∂ / ∂y (4z) = 0

∂ / ∂y (3x^{2}y) = 0

∂ / ∂x (4z) = 0

∂ / ∂x (5xy^{2}) = 0

∂ / ∂z (5xy^{2}) = 5y^{2}

∂ / ∂z (3x^{2}y) = 3x^{2}

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

curl(3x^{2}y + 5xy^{2} + 4z) = (0, 0, -3x^{2} + 5y^{2})

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

curl(3x^{2}y + 5xy^{2} + 4z)_{(5, 7, 6) }= (0, 0, 170)