Effects of Water on Magnetic Field Outside a Finite Solenoid?

In summary, the conversation discusses the difficulty of calculating the magnetic field outside a real finite solenoid and offers suggestions and methods for finding the field using Ampere's law and the Biot-Savart law. The conversation also mentions the use of integral forms and equations to calculate the field and suggests resources for further information on the topic. The conversation ends with a question about the effect of water on the magnetic field.
  • #1
bjornmag
1
0
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
 
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  • #2
bjornmag said:
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.
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
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
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:
  • #5
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
Great post Miller. However i think you are wrong.

What happens when water is introduced?
 

1. What is a short solenoid?

A short solenoid is a cylindrical coil of wire that produces a magnetic field when an electric current is passed through it. It is typically shorter in length compared to a long solenoid.

2. How is the magnetic field outside a short solenoid calculated?

The magnetic field strength outside a short solenoid can be calculated using the formula B = μ₀nI, where B is the magnetic field strength, μ₀ is the permeability of free space, n is the number of turns per unit length of the solenoid, and I is the current passing through the solenoid.

3. Is the magnetic field outside a short solenoid uniform?

No, the magnetic field strength outside a short solenoid is not uniform. The strength of the magnetic field decreases as the distance from the solenoid increases, and the field is strongest at the ends of the solenoid.

4. How does the direction of the magnetic field outside a short solenoid change?

The direction of the magnetic field outside a short solenoid depends on the direction of the current passing through the solenoid. If the current is flowing clockwise, the magnetic field will point towards the solenoid, and if the current is flowing counterclockwise, the magnetic field will point away from the solenoid.

5. What are some practical applications of a short solenoid?

Short solenoids have various practical applications, such as in electromagnets, motors, generators, and speakers. They are also used in magnetic resonance imaging (MRI) machines, particle accelerators, and magnetic levitation systems.

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