# Is the magnetic field inside a solenoid stronger near the border?

• Rafikix
In summary: The field is most uniform in the center. It is strongest near the coil.... from my intuition I thought they were stronger in the center...
Rafikix
I was reading some papers about calculating the magnetic field produced by a coil using the biot savart law and I saw some graphs that caught my attention.

This one from a paper from Ravaud, et al. Titled "Calculation of the Magnetic Field Created by a Thick Coil". I saw similar graphs in other articles too.

And this one from the wikipedia entry for solenoids.

They seem to indicate that the magnetic field gets stronger near the border, whereas from my intuition I thought they were stronger in the center.
I also did a simulation in python using the biot savart law and the formula from Ravaud's paper and the plot looked like the wikipedia's one, with the magnetic field stronger nearing the border with that triangular shape.

How do I explain this?

By "border" you mean coils? Yes, the field is strong near the coils.

Rafikix said:
The center of the coil is at r=0...that would be about a foot off the side of my monitor. This is in a tenth inch thick wire turn I beleive.

Rafikix said:
whereas from my intuition I thought they were stronger in the center.
My intuition is that the coils are the source and the field always gets weaker as you go away from them. I will try to think of a proof.

For a long straight wire the field falls off as 1/r. If you get close enough everything is flat...
You mean coil center or wire center ?

Rafikix said:
They seem to indicate that the magnetic field gets stronger near the border, whereas from my intuition I thought they were stronger in the center.
The field is most uniform in the center. It is strongest near the coil.

Rafikix and vanhees71
Rafikix said:
... from my intuition I thought they were stronger in the center...
To test intuitions consider extreme cases: Increase the radius of the coil towards infinity while keeping its axial length constant. Does your intuition still say that the field will be strongest in the middle, far far away from the conducting wire loop?

Last edited:
Rafikix

## 1. Is the magnetic field inside a solenoid stronger near the border?

Yes, the magnetic field inside a solenoid is stronger near the border. This is because the magnetic field lines are closer together near the border, resulting in a stronger magnetic field.

## 2. How does the strength of the magnetic field inside a solenoid vary near the border?

The strength of the magnetic field inside a solenoid varies near the border in a non-linear manner. It increases rapidly as you move closer to the border and then levels off as you reach the center of the solenoid.

## 3. What factors affect the strength of the magnetic field inside a solenoid near the border?

The strength of the magnetic field inside a solenoid near the border is affected by the number of turns in the coil, the current flowing through the solenoid, and the material of the core. Increasing any of these factors will result in a stronger magnetic field near the border.

## 4. Can the strength of the magnetic field inside a solenoid be increased near the border?

Yes, the strength of the magnetic field inside a solenoid can be increased near the border by increasing the number of turns in the coil, increasing the current flowing through the solenoid, or using a material with a higher magnetic permeability for the core.

## 5. How does the shape of the solenoid affect the strength of the magnetic field near the border?

The shape of the solenoid does not have a significant effect on the strength of the magnetic field near the border. As long as the solenoid is long and thin, the magnetic field will be stronger near the border compared to the center of the solenoid.

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