Note on ‘‘Magnetic field due to a solenoid’’

The evaluation of the magnetic field inside and outside a uniform current density infinite solenoid of uniform cross-section is an elementary problem in classical electrodynamics that all undergraduate Physics students study. Symmetry properties of the cylinder and the judicious use of Ampere's circuital law leads to correct results; however it does not explain why the field is non zero for a finite length solenoid, and why it vanishes as the solenoid becomes infinitely long. An argument

Section: Introductionmentioning

confidence: 99%

An elementary argument for the magnetic field outside a solenoid

Pathak¹

2016

“…However, being conservative, the deviation of (29) In addition to the widely studied axial and radial components, e.g. [8,[28][29][30][31][32][33][34][35][36][37][38][39], the magnetic field generated by a tightly wound solenoid has a weaker azimuthal component which can be readily evaluated, an analysis which has hitherto been restricted to the infinitely long solenoid [16][17][18][19][20][21][22][23][24][25].…”

Section: Extension To Z C > L=2mentioning

confidence: 99%

Using Biot–Savart’s law to determine the finite tube’s magnetic field

Ferreira

Anacleto

2018

Biot-Savart's law is used to determine in all regions of space the magnetic field generated by a finite length conducting tube of negligible thickness. Simplified approximate closed form solutions for the magnetic field in the tube axis vicinity, near the median plane just outside the tube, and very far from the tube, are also derived. Lastly, the finite tubular conductor results are used to address the finite solenoid magnetic field's azimuthal component.

An approach to the magnetic field of a finite solenoid with a circular cross-section

Lin

2021

We present a simple approach, different from approaches in the literature, for calculating the magnetic field of a finite solenoid with a circular cross section, carrying an ideal surface current with an ordinary azimuthal component and a small axial component due to nonideal winding. The results are given as an infinite series whose terms are elementary functions or simple polynomials rather than other infinite series. It is easy to deal with the results because the polynomials involved are partial binomial expansions. These series converge rapidly everywhere, except near the edges of the solenoid. From these results, it is very easy to derive some general properties of the magnetic field, to reduce the field to greatly simplified forms in various special regions, and to address the special cases of infinite and semi-infinite solenoids. The azimuthal field due to nonideal winding is shown to be small everywhere. A solenoid with a small but finite thickness in the radial direction is investigated in detail, and we present simple analytic approximate results for its magnetic field. A comparison with an exact numerical evaluation shows that these are very good approximations.