Curl Calculator

The curl calculator makes way for visualization of the curl of a vector field. The curl of a given vector field A is denoted by curl A or ∇ x A. It is a vector whose magnitude is the maximum net circulation of A per unit area.

This is because the area tends to zero and one whose direction is the normal direction of the area when the area is oriented to make the net circulation maximum.

The steps to use this calculator is:

1. You must enter in the x and y components of your vector field as functions of x and y.

2. Eventually, the top graph shows the magnitude of the curl as a surface plot. So, a positive magnitude indicates a curl pointed out of the screen and a negative magnitude indicates a curl pointed into the screen.

3.  Finally, the bottom graph shows the vector field that you are taking the curl of.

The physical significant indication of the curl of a vector field is the amount of “rotation” or angular momentum of the contents of the given region of space. It so arises in fluid mechanics and elasticity theory.

This theory is also fundamental in the theory of electromagnetism, wherein it arises in two of the four Maxwell equations.

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