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Enter functions and points to the required fields and hit the calculate button to use this curl calculator
Table of Contents:
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.
The curl formula is shown below,
- “∇” This sign is called Nabla.
- A (Ax, Ay, Az) 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:
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.
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?
Find the curl of the given function F = (3x2y + 5xy2 + 4z) with the given points (5, 7, 6)
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)