Curl

Curl is a term used in various contexts in mathematics and physics. In vector calculus, it is a vector operator that describes the infinitesimal rotation of a 3-dimensional vector field. In physics, it is used to define the rotation of a field, such as the magnetic or velocity fields.

Definition[edit | edit source]

In vector calculus, the curl is a vector operator that describes the infinitesimal rotation of a 3-dimensional vector field. At every point in the field, the curl of that point is represented by a vector. The attributes of this vector (length and direction) characterize the rotation at that point.

The curl of a vector field F, denoted by curl F, or ∇ × F, is defined as the vector field having magnitude equal to the maximum "circulation" at each point and to be oriented perpendicularly to this plane of circulation for each point.

Mathematical Formulation[edit | edit source]

The curl of a vector field F, denoted by curl F or ∇ × F, is defined using the del operator (∇) and the cross product (×). The curl of F is given by:

∇ × F = ( ∂Fz/∂y - ∂Fy/∂z ) i + ( ∂Fx/∂z - ∂Fz/∂x ) j + ( ∂Fy/∂x - ∂Fx/∂y ) k

where i, j, and k are the unit vectors for the x, y, and z directions, respectively.

Physical Interpretation[edit | edit source]

In physics, the curl of a field is used to determine the rotation of that field. For example, the curl of a velocity field gives the vorticity, or the local spinning motion of a fluid near some point, as opposed to the motion of the fluid at that point.

References[edit | edit source]

Curl Resources
Need Help Finding a Doctor? Need help finding a doctor or specialist anywhere in the world? Explore our world directory. WikiMD's DocFinder can assist you in locating millions of physicians.	Medical Knowledge Access the latest research - Most recent articles Ongoing trials.