# How do you calculate magnetic field stregth outside a solenoid?

1. Aug 6, 2010

### rsalmon

Hi,

I've have been searching for help in calculating the magnetic field strength at any given position outside a solenoid.
I can use Biot-Savart's to get the field along the axis of the solenoid but how does the field vary perpendicular to the axis of the solenoid, for example.

Rob

2. Aug 6, 2010

### Bob S

The vector potential and the components of the field everywhere outside a single current loop is given by Smythe Static and Dynamic Electricity Third Edition, page 291, in terms of elliptic integrals. The field of a multiturn solenoid can be calculated using numerical integration. The fields can also be calculated using expressions involving Legendre polynomials on pages 293-4. I cannot find any closed-form expression for the off-axis field for a multi-turn solenoid. The on-axis field is given by the closed-from expression

http://www.netdenizen.com/emagnet/solenoids/thinsolenoid.htm

Bob S

3. Aug 9, 2010

### rsalmon

Ok thanks Bob,
I had a look at the text and this is going to call for a simple(ish) computer code. In fact I have found a magnetic field calculator at this site

http://vizimag.com/calculator.htm

This says it does the fields outside and off axis. though haven't tried it yet, waiting for admin to let me install it.

Thanks again. Rob

4. Aug 9, 2010

### Bob S

Rsalmon-
The equation for the magnetic field near an aircore solenoid used by Visimag seems to be correct. It uses both elliptic integrals E(θ) and K(θ), as shown in Smythe. The series expansions for these elliptic integrals are in Dwight Tables of Integrals (Macmillan, 1947), paragraphs 773 and 774 on page 171. The recursion formulas for these series expansions are simple, and the integrals can be easily evaluated in a short subroutine.

Bob S