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Curl

The document explains the concept of curl in vector calculus, defining it as the cross product of the vector operator ∇ with a differentiable vector field F. It provides the mathematical representation of curl F in terms of its components. Additionally, it notes that if curl F equals zero, the vector field F is considered irrotational.

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29 views1 page

Curl

The document explains the concept of curl in vector calculus, defining it as the cross product of the vector operator ∇ with a differentiable vector field F. It provides the mathematical representation of curl F in terms of its components. Additionally, it notes that if curl F equals zero, the vector field F is considered irrotational.

Uploaded by

balaji
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
Available Formats
Download as PDF, TXT or read online on Scribd
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Calculus

Curl

Curl of a Vector

Let F (x, y, z) is a vector field defined for all (x, y, z) in a certain region of space and
is differentiable i.e., F is a differential vector field. The cross product of the vector
operator ∇ with the vector F is termed as curl F .
î ĵ k̂
∂ ∂ ∂ ∧ ∧ ∧
curl F=
∂x ∂y ∂z ; F = F1 i + F2 j + F3 k
F1 F2 F3

Note: If curl F = 0, then F is said to be irrotational.

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