HiI know that for a short solenoid (L<R) the magnetic field at the

In summary, the conversation discusses the formula for calculating magnetic field at the axis of a short solenoid, and the question of whether this formula can be applied to a solenoid with multiple turns in each vertical plane. The answer is that one can simply add the field for each individual turn in this case, but the formula is still applicable for any length of solenoid.
  • #1
Niles
1,866
0
Hi

I know that for a short solenoid (L<R) the magnetic field at the axis is (standard EM)
[tex]
B(z) = \frac{1}{2}\mu_0 \frac{N}{L}I(\frac{z+\frac{L}{2}}{\sqrt{(z+L/2)^2+R^2}} - \frac{z-\frac{L}{2}}{\sqrt{(z-L/2)^2+R^2}})
[/tex]
where R is the radius of the solenoid, N the number of turns along the axis and L the length. In this system, each vertical plane consists of a single turn, but say I am looking at a solenoid, where each vertical plane consists of e.g. 2 turns. First I thought about using the above equation twice, but that is wrong since it is not 2 independent solenoids.

Is it correct to regard the system simply as a collection of coils with 2 turns each? I'm not quite sure how this would work out, since this way I can't take into account the widths of each individual coil. If my description is confusing, please let me know.Niles.
 
Last edited:
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  • #2


Your formula is for a solenoid of any length, not just L<R.
I don't understand what you mean be 'two turns'.
Why would it make a difference?
 
  • #3


Hi, thanks for replying. I really appreciate it. What I mean by two turns is the following:

OOOOOO
OOOOOO
------------ (axis of solenoid)
OOOOOO
OOOOOO

There I have a solenoid with 12 turns in total, i.e. a 6-turn solenoid on top of another (larger radii) 6-turn solenoid. How would one calculate the B-field for that? In principle I could just add the B-field for each one of the 12 turns, right? The reason why I am asking is because I am looking for the most general way to calculate this, because I would also have to look at e.g.OOOO
OOOOOO
OOOOOOOO
---------------------- (axis)
OOOOOOOO
OOOOOO
OOOO
 

1. What is a solenoid?

A solenoid is a coil of wire that is used to generate a magnetic field when an electric current is passed through it. It is a common component in many electronic devices such as motors, speakers, and relays.

2. What is the relationship between the length and radius of a solenoid?

The length and radius of a solenoid are directly proportional. This means that as the length of the solenoid increases, so does its radius. This relationship is important because it affects the strength and uniformity of the magnetic field produced by the solenoid.

3. How does the magnetic field in a solenoid change with length?

The magnetic field in a solenoid is directly proportional to its length. This means that as the length of the solenoid increases, so does the strength of its magnetic field. However, this relationship is only true for short solenoids (L < R). For longer solenoids, the magnetic field reaches a maximum and then starts to decrease as the length increases.

4. What is the purpose of a short solenoid in scientific experiments?

In scientific experiments, a short solenoid is often used to produce a strong and uniform magnetic field. This is because the magnetic field in a short solenoid is directly proportional to its length, making it easier to control and manipulate. Short solenoids are commonly used in particle accelerators, MRI machines, and in experiments that study the behavior of charged particles in a magnetic field.

5. How does the magnetic field in a short solenoid compare to that of a long solenoid?

The magnetic field in a short solenoid is stronger and more uniform compared to that of a long solenoid. This is because the magnetic field in a short solenoid is directly proportional to its length, while in a long solenoid it reaches a maximum and then decreases. This makes short solenoids more useful in scientific experiments and applications that require a strong and uniform magnetic field.

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