**ERIC Number:**EJ1046777

**Record Type:**Journal

**Publication Date:**2014-Dec

**Pages:**1

**Abstractor:**As Provided

**ISBN:**N/A

**ISSN:**ISSN-0031-921X

**EISSN:**N/A

Magnetic Fields at the Center of Coils

Binder, Philippe; Hui, Kaleonui; Goldman, Jesse

Physics Teacher, v52 n9 p560 Dec 2014

In this note we synthesize and extend expressions for the magnetic field at the center of very short and very long current-carrying coils. Elementary physics textbooks present the following equation for the magnetic field inside a very long current-carrying coil (solenoid): B[subscript sol] = µ[subscript 0] (N/L) I, (1) where I is the current, N the number of windings, and L the coil length. It is obtained directly from Ampère's law, ignores end effects (hence it assumes an infinite coil), and is valid over the entire cross-section of the coil. The field is in the axial direction and it follows the right-hand rule convention. For N superposed loops of radius R each carrying current I, the multi-loop magnetic field at the center is given by B[subscript ml] = µ[subscript 0] (N/2R) I. (2)

Descriptors: Science Instruction, Magnets, Physics, Equations (Mathematics), College Science, Undergraduate Study, Textbooks, Scientific Concepts

American Association of Physics Teachers. One Physics Ellipse, College Park, MD 20740. Tel: 301-209-3300; Fax: 301-209-0845; e-mail: pubs@aapt.org; Web site: http://scitation.aip.org/tpt

**Publication Type:**Journal Articles; Reports - Research

**Education Level:**Higher Education; Postsecondary Education

**Audience:**N/A

**Language:**English

**Sponsor:**N/A

**Authoring Institution:**N/A

**Grant or Contract Numbers:**N/A