Magnetic field outside a solenoid

In summary, the magnetic field outside a solenoid of very long length can be assumed to be near zero. Far away from the solenoid, the magnetic field of the far side will tend to cancel the field of the near side. However, inside the solenoid, the fields will add up, leading to a much stronger field.
  • #1
SteveDC
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I am trying to understand why the magnetic field outside a solenoid of very long length can be assumed to be near zero.

I gather that the field inside the solenoid will be very dense and therefore strong, and that the field lines that loop back round outside the solenoid can spread out. Is this the correct understanding.

If so why do the field lines spread out outside the solenoid so much so that their density tends to zero as the solenoid gets longer?
 
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  • #2
It's just an approximation.

Think about an electric dipole in one dimension. Far away from the dipole the effect of both particles will tend to cancel out because they subtract. Right in the middle of the dipole the field will be strong because they add.

Outside of the solenoid the magnetic field of the far side will tend to cancel the field of the near side. The further you get the weaker the field. It will actually drop off fairly quick. Inside the solenoid the fields will add up.
 
  • #3
Hi SteveDC! :smile:
SteveDC said:
I gather that the field inside the solenoid will be very dense and therefore strong, and that the field lines that loop back round outside the solenoid can spread out. Is this the correct understanding.

yes :smile:
If so why do the field lines spread out outside the solenoid so much so that their density tends to zero as the solenoid gets longer?

the densest flux comes out of the centre of the solenoid

flux near the rim of the solenoid is least dense, and that's the flux that takes the shortest way round, ie nearest to the solenoid

so the flux at any small distance r from the outside of the solenoid will be weak

if you fix r, and increase the length of the solenoid, the lines that go through r will get closer to the rim of the solenoid …

at infinite length, they're infinitesimally close to the rim, and their density approaches zero :wink:

to put it another way, there's only so many field lines, no matter how long the solenoid is

those field lines have to follow the same graceful curves

so they get infinitely far away from the solenoid! :wink:
 

What is a solenoid and how does it create a magnetic field?

A solenoid is a coil of wire that carries an electric current. When an electric current flows through the wire, it creates a magnetic field around the solenoid. This is due to the interaction between the moving charges in the wire and the magnetic field they produce.

What is the direction of the magnetic field outside a solenoid?

The direction of the magnetic field outside a solenoid depends on the direction of the electric current flowing through the wire. Using the right-hand rule, the fingers of your right hand point in the direction of the electric current, and your thumb points in the direction of the magnetic field outside the solenoid.

How does the strength of the magnetic field outside a solenoid change with distance?

The strength of the magnetic field outside a solenoid decreases as you move further away from the solenoid. This is because the magnetic field lines spread out as they travel away from the solenoid, resulting in a weaker field at a greater distance.

Can the magnetic field outside a solenoid be manipulated?

Yes, the magnetic field outside a solenoid can be manipulated by changing the current flowing through the wire or by using materials such as iron to concentrate and strengthen the field. Additionally, by changing the number of turns in the wire or the radius of the solenoid, the strength and direction of the magnetic field can also be altered.

What are some real-life applications of a magnetic field created by a solenoid?

The magnetic field created by a solenoid has a wide range of practical applications, such as in electromagnets used in motors, generators, and speakers. It is also used in MRI machines in medical imaging, as well as in particle accelerators and mass spectrometers in scientific research.

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