curl

(noun)

the vector field denoting the rotationality of a given vector field

Related Terms

Examples of curl in the following topics:

  • Curl and Divergence

    • The four most important differential operators are gradient, curl, divergence, and Laplacian.
    • At every point in the field, the curl of that field is represented by a vector.
    • The direction of the curl is the axis of rotation, as determined by the right-hand rule, and the magnitude of the curl is the magnitude of rotation.
    • A vector field whose curl is zero is called irrotational.
    • The curl is a form of differentiation for vector fields.

  • Stokes' Theorem

    • Stokes' theorem relates the integral of the curl of a vector field over a surface to the line integral of the field around the boundary.
    • The Kelvin–Stokes theorem, also known as the curl theorem, is a theorem in vector calculus on $R^3$.
    • Given a vector field, the theorem relates the integral of the curl of the vector field over some surface to the line integral of the vector field around the boundary of the surface.

  • Conservative Vector Fields

    • Conservative vector fields are also irrotational, meaning that (in three dimensions) they have vanishing curl.
    • Therefore, the curl of a conservative vector field $\mathbf{v}$ is always $0$.
    • A vector field $\mathbf{v}$, whose curl is zero, is called irrotational .
    • However, any simply connected subset that excludes the vortex line $(0,0,z)$ will have zero curl, $\nabla \mathbf{v}=0$.

  • Hydrostatics

    • Let's take the curl of both sides to get

  • Angular Quantities as Vectors

    • Using this right hand rule, the direction of angular velocity ω and angular momentum L are defined as the direction in which the thumb of your right hand points when you curl your fingers in the direction of the disc's rotation.
    • The direction of angular velocity ω size and angular momentum L are defined to be the direction in which the thumb of your right hand points when you curl your fingers in the direction of the disk's rotation as shown.

  • Sculpture in Southeast Asia

    • Symbolic shell-like curls were used to render the hair of the Buddha.
    • Sculpted in the Mon Dwaravati style, this bronze statue has an idealized rather than realistic physical form including shell like curls for hair.

  • Electric vs. Magnetic Forces

    • The curl of the electric force is zero, i.e.:
    • One can see clearly that the curl of the electric force is zero .
    • The curl of a magnetic field generated by a conventional magnet is therefore always non zero.

  • Chemotherapy and Hair Loss

    • It is more common for the hair to grow back curlier, producing what are called "chemo curls. " Occasionally, the hair loss from chemotherapy can be permanent.

  • Ampere's Law: Magnetic Field Due to a Long Straight Wire

    • As illustrated in the direction of the magnetic field can be determined using the right hand rule—pointing one's thumb in the direction of current, the curl of one's fingers indicates the direction of the magnetic field around the straight wire.

  • Magnetic Force on a Current-Carrying Conductor

    • Curling the fingers reveals the direction of magnetic force.