### Abstract

It has been widely acknowledged that there is some discrepancy in the teaching of vector calculus in mathematics courses and other applied fields. The curl of a vector field is one topic many students can calculate without understanding its significance. In this paper, we explain the origin of the curl after presenting the standard mathematical formulas. We investigate when and why a vector field yields an in-spot spin, also known as curl, and develop intuition to predict the sign of the curl of a vector field without calculating it. As an application of the curl, Stokes' theorem and its physical interpretation are presented with simple illustrations.

Original language | English |
---|---|

Pages (from-to) | 275-287 |

Number of pages | 13 |

Journal | PRIMUS |

Volume | 16 |

Issue number | 3 |

DOIs | |

State | Published - 1 Jan 2006 |

### Fingerprint

### Keywords

- Curl
- Paddle wheel
- Spin
- Vector field

### Cite this

*PRIMUS*,

*16*(3), 275-287. https://doi.org/10.1080/10511970608984151

}

*PRIMUS*, vol. 16, no. 3, pp. 275-287. https://doi.org/10.1080/10511970608984151

**The curl of a vector field : Beyond the formula.** / Burch, Kimberly Jordan; Choi, Youngna.

Research output: Contribution to journal › Article

TY - JOUR

T1 - The curl of a vector field

T2 - Beyond the formula

AU - Burch, Kimberly Jordan

AU - Choi, Youngna

PY - 2006/1/1

Y1 - 2006/1/1

N2 - It has been widely acknowledged that there is some discrepancy in the teaching of vector calculus in mathematics courses and other applied fields. The curl of a vector field is one topic many students can calculate without understanding its significance. In this paper, we explain the origin of the curl after presenting the standard mathematical formulas. We investigate when and why a vector field yields an in-spot spin, also known as curl, and develop intuition to predict the sign of the curl of a vector field without calculating it. As an application of the curl, Stokes' theorem and its physical interpretation are presented with simple illustrations.

AB - It has been widely acknowledged that there is some discrepancy in the teaching of vector calculus in mathematics courses and other applied fields. The curl of a vector field is one topic many students can calculate without understanding its significance. In this paper, we explain the origin of the curl after presenting the standard mathematical formulas. We investigate when and why a vector field yields an in-spot spin, also known as curl, and develop intuition to predict the sign of the curl of a vector field without calculating it. As an application of the curl, Stokes' theorem and its physical interpretation are presented with simple illustrations.

KW - Curl

KW - Paddle wheel

KW - Spin

KW - Vector field

UR - http://www.scopus.com/inward/record.url?scp=84978797457&partnerID=8YFLogxK

U2 - 10.1080/10511970608984151

DO - 10.1080/10511970608984151

M3 - Article

AN - SCOPUS:84978797457

VL - 16

SP - 275

EP - 287

JO - PRIMUS

JF - PRIMUS

SN - 1051-1970

IS - 3

ER -