# Field outside short solenoid

1. Mar 2, 2005

### bjornmag

I can`t seem to find any information on how to calculate the magnetic field outside a real finite solenoid. I do not need the field on-axis, but rather perpendicular to the solenoid. Any ideas on how to proceed, or suggestions to literature?

Thanks

Indian

2. Mar 2, 2005

### Andrew Mason

You just have to use Ampere's law and add the field of all the loops in the solenoid. For a short solenoid, you can approximate with a single loop with total current = NI where N is the number of turns. But you can see that it is similar to the field some distance from two parallel wires with currents in opposite directions (ie at a distance d>>s where s is the separation between the wires) which is effectively 0 because the fields cancel.

AM

3. Aug 17, 2005

### Miller278

Ampere's law is only useful for finding the magnetic field around either a toroidal (i.e. donut) solenoid or an ideal (i.e. infinitely long, infinitely thin) solenoid, where the field is indeed zero. Outside a finite solenoid this is definitely not true (since a current outside a bar electromagnet would experience a force), at present I am trying to derive the equations from the Biot-Savart law for the magnetic field at any point around a single current loop (a solenoid with one loop and neglidgeable length). I will put these on the forum when I can (note: they will probably be in integral form), hopefully this will prove helpful.

4. Aug 18, 2005

### Miller278

O.K. so far as I know this is the equation for magnetic field at any point around a single loop of wire in the x-y plane carrying current I where your position p relative to the centre of the loop is given by:
p =xi +yj +zk , at that point the magnetic field B is given by the equation in the linked page. Unfortunately this equation is still in integral form, I will attempt to convert it into normal equation form asap.
This maybe used to give the b-field around a short solenoid by treating it as a series of rings and adding up the magnetic fields caused by each ring by using offset values of z in the attached equation (i.e. for a ring half a metre above the x-y plane change z to z-0.5 in the equation).
I hope this is useful.

http://img.photobucket.com/albums/v115/losseniaiel/b-field.jpg

Last edited: Aug 18, 2005
5. Aug 18, 2005

### Meir Achuz

The B field due to a current loop is given in Sect. 5.5 of Jackson "Classical Electrodynamics" and in Sect. 7.10.1 of Franklin "Classical Electromagnetism.
Similar methods can be used to find the field outside a finite solenoid.

6. Aug 18, 2005

### PHILIE-T

Great post Miller. However i think you are wrong.

What happens when water is introduced?