Calculating Torque on Magnet in Solenoid

• alan3303
In summary: Inside the solenoid is a rare Earth bar magnet of some length, initial mis alignment (degrees). The magnet is only free to rotate. Bob has the manufactures information for the magnet seen below. remanence (Br), which measures the strength of the magnetic field = 1.2 teslasenergy product (BHmax), the density of magnetic energy = 300 Kj/m^3 In summary, the magnetic moment of the bar magnet is p = qmL, and the torque is τ = p x B.
alan3303
I am a mechanical engineer and am having to do some calculations concerning magnets and solenoids for a project I am on.

I have a solenoid (defined by number loops, current and cross sectional area).

Inside the solenoid is a rare Earth bar magnet of some length, initial mis alignment (degrees). The magnet is only free to rotate. I have the manufactures information for the magnet seen below.
remanence (Br), which measures the strength of the magnetic field = 1.2 teslas
energy product (BHmax), the density of magnetic energy = 300 Kj/m^3

How do I calculate the torque on this magnet when the solenoid is turned on? I have looked and looked online but I don't know how to convert the manufactures data into a magnetic moment or a magnetic field or anything else I could find of use.

Please any help would be greatly appreciated I have already spent way to much time on this.

Thanks,

alan3303 said:
I am a mechanical engineer and am having to do some calculations concerning magnets and solenoids for a project I am on.

I have a solenoid (defined by number loops, current and cross sectional area).

Inside the solenoid is a rare Earth bar magnet of some length, initial mis alignment (degrees). The magnet is only free to rotate. I have the manufactures information for the magnet seen below.
remanence (Br), which measures the strength of the magnetic field = 1.2 teslas
energy product (BHmax), the density of magnetic energy = 300 Kj/m^3

How do I calculate the torque on this magnet when the solenoid is turned on? I have looked and looked online but I don't know how to convert the manufactures data into a magnetic moment or a magnetic field or anything else I could find of use.

Please any help would be greatly appreciated I have already spent way to much time on this.

Thanks,

Welcome to the PF. The way I have it pictured in my head, there will be no torque on the bar inside the solenoid coil. Their magnetic fields are parallel or anti-parallel. You may get some force pushing the magnet either partially out or all the way out of the solenoid, and you may partially demagnitize the magnet (if the 2 fields are anti-parallel), but I don't see a torque anywhere (except maybe from the few degrees of misalignment you mention).

Could you post a picture, and describe the moment arm and where the force would be applied to give you a torque?

I plan on ensuring the mis-alignment to be somewhat large to induce the needed torque. I need to be able to rotate the magnet 40-60 degrees one way and then reverse the solenoid and rotate it back to the original positions. I am curious at my minimum mis alignment how much torque can I get probably between 10 and 30 degrees.

alan3303 said:
I plan on ensuring the mis-alignment to be somewhat large to induce the needed torque. I need to be able to rotate the magnet 40-60 degrees one way and then reverse the solenoid and rotate it back to the original positions. I am curious at my minimum mis alignment how much torque can I get probably between 10 and 30 degrees.

The magnetic "charge" qm of a bar magnet pole is given in Eqn (1) in

http://instruct.tri-c.edu/fgram/WEB/Mdipole.htm

The dipole moment of the bar magnet is p = qmL where L is the length of the bar magnet

the torque is τ = p x B

where p x B is the vector cross product (= the magnitude of p and B times the sine of the included angle), and B is the magnetic field inside the solenoid.

If you know the moment of inertia of the magnet, you can calculate the oscillation period of the magnet in the solenoid.

I could help you more if you give complete details of both the bar magnet and the solenoid.

Do all of your calculations in mks units, and you will get the torque in Newton-meters.

Bob S

Last edited by a moderator:

1. What is the formula for calculating torque on a magnet in a solenoid?

The formula for calculating torque on a magnet in a solenoid is T = N * I * A * B * sin(theta), where T is the torque, N is the number of turns in the solenoid, I is the current flowing through the solenoid, A is the area of the solenoid, B is the magnetic field strength, and theta is the angle between the magnetic field and the area of the solenoid.

2. How does changing the current affect the torque on the magnet in a solenoid?

As the current flowing through the solenoid increases, the torque on the magnet also increases. This is because the magnetic field produced by the solenoid becomes stronger, resulting in a larger force acting on the magnet and creating a greater torque.

3. What is the role of the number of turns in the solenoid in calculating torque?

The number of turns in the solenoid affects the strength of the magnetic field produced. As the number of turns increases, the magnetic field becomes stronger, resulting in a larger torque on the magnet.

4. Can the angle between the magnetic field and the area of the solenoid affect the torque on the magnet?

Yes, the angle between the magnetic field and the area of the solenoid can affect the torque on the magnet. The torque is maximum when the angle is 90 degrees, and decreases as the angle approaches 0 or 180 degrees.

5. How can I increase the torque on the magnet in a solenoid?

To increase the torque on the magnet in a solenoid, you can increase the current flowing through the solenoid, increase the number of turns in the solenoid, or increase the area of the solenoid. Additionally, changing the angle between the magnetic field and the area of the solenoid to be closer to 90 degrees can also increase the torque.

• Electrical Engineering
Replies
7
Views
2K
• Electromagnetism
Replies
3
Views
1K
• Electromagnetism
Replies
5
Views
1K
• Electrical Engineering
Replies
8
Views
2K
• Introductory Physics Homework Help
Replies
3
Views
96
• Electrical Engineering
Replies
4
Views
1K
• Introductory Physics Homework Help
Replies
41
Views
3K
• Electrical Engineering
Replies
14
Views
4K
• Electromagnetism
Replies
21
Views
1K
• Electrical Engineering
Replies
4
Views
3K