Effects of Water on Magnetic Field Outside a Finite Solenoid?

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SUMMARY

This discussion focuses on calculating the magnetic field outside a finite solenoid, particularly perpendicular to its axis. Participants emphasize the use of Ampere's law and the Biot-Savart law for deriving the magnetic field equations. The magnetic field can be approximated by treating the solenoid as a series of current loops, and the relevant equations can be found in "Classical Electrodynamics" by Jackson and "Classical Electromagnetism" by Franklin. The introduction of water's effects on the magnetic field remains unexplored in this discussion.

PREREQUISITES
  • Understanding of Ampere's law
  • Familiarity with the Biot-Savart law
  • Knowledge of magnetic fields generated by current loops
  • Basic concepts of electromagnetism
NEXT STEPS
  • Research the application of the Biot-Savart law for finite solenoids
  • Study the effects of dielectric materials, such as water, on magnetic fields
  • Examine the derivation of magnetic field equations from current loops
  • Explore advanced topics in electromagnetism, particularly in finite solenoid configurations
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Students and professionals in physics, electrical engineering, and anyone interested in the behavior of magnetic fields around finite solenoids and their interactions with materials like water.

bjornmag
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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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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
 
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.
 
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:
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.
 
Great post Miller. However i think you are wrong.

What happens when water is introduced?
 

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