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Curl Calculator
To find the curl through curl calculator, Select the method of your input i.e., with points or without points, enter the functions, and click calculate button
Curl Calculator
Curl Calculator is used to find the curl of a vector field at the given points of function x, y, and z. This curl finder will take three functions along with their points to find the curl of a vector with steps.
What is the curl of a vector?
The curl of a vector is defined as the cross-product of a vector with nabla ∇. The curl is a vector quantity. Geometrically, the curl of a vector gives us information about the tendency of a field to rotate about a point.
Formula of the curl
∇ × F = ( ∂/∂y [R] - ∂/∂z [Q], ∂/∂z [P] - ∂/∂x [R], ∂/∂x [Q] - ∂/∂y [P])
Where
- ∇ is known as the nabla operator and G is the function.
- G= G(x1, x2, x3)
- $$∇=\frac{\partial }{\partial x},\:\frac{\partial }{\partial y},\:\frac{\partial }{\partial z}$$
The determinant is taken as:
$$∇\cdot G=\left[\frac{\partial \:\:}{\partial y}\left(G_3\right)-\frac{\partial \:\:}{\partial z}\left(G_2\right)\right]i\:-\left[\frac{\partial \:\:}{\partial x}\left(G_3\right)-\frac{\partial \:\:}{\partial z}\left(G_1\right)\right]j+\left[\frac{\partial \:\:}{\partial x}\left(G_2\right)-\frac{\partial \:\:}{\partial y}\left(G_1\right)\right]k$$
How we find the curl of a vector:
To find the curl of a vector we have to understand the step-by-step solutions with the help of an example.
Example:
Find the curl of a three-dimensional vector: F = (xy, tan(x), e^z) at the point (2,3,4).
Solution:
Step 1: By definition of curl, we have to take the determinant
$$∇\cdot G=\left[\frac{\partial \:\:}{\partial y}\left(e^z\right)-\frac{\partial \:\:}{\partial z}\left(tan\left(x\right)\right)\right]i\:-\left[\frac{\partial \:\:}{\partial x}\left(e^z\right)-\frac{\partial \:\:}{\partial z}\left(xy\right)\right]j+\left[\frac{\partial \:\:}{\partial x}\left(tan\left(x\right)\right)-\frac{\partial \:\:}{\partial y}\left(xy\right)\right]k$$
Step 2: Now take the partial derivatives
∂/∂y (ez) = 0
∂/∂z (tan(x)) = 0
∂/∂x (ez) = 0
∂/∂z (xy) = 0
∂/∂x (tan(x)) = sec2(x)
∂/∂y (xy) = x
Step 3: Now put the values of partial derivatives in the formula:
(0, 0, -x + sec2(x))
Step 4: Now put the value of the point in the function.
(0, 0, -2 + sec2(2))
Hence we have a curl -2+sec2(2) of the vector.
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