# How Is Work Calculated for Permanent Magnets on Iron Plates?

• korneld
In summary: Is that correct?No. The force is proportional to the surface area, so the thickness of the object is not an issue.
korneld
Hi,

I have two questions about permanent magnets:

1. How do you calculate the work done by a permanent magnet on, say, an iron plate?

2. I am aware that the force exerted on an object by a magnet depends on the surface area. Is it also affected by the thickness of the object to a certain extent? What is the minimum thickness after which thickness is not an issue?

Thanks.

The work is force times distance (when linear) or better, the integral of force to the distance it acted upon.

Thickness of what, the metal plate of the magnet.

Thanks for that.

But the problem is that the force increases as the distance between the objects decreases. I thought there might be a formula that takes the increasing flux into account.

It is an inverse-square relationship between distance and force.

Btw, your OP asks about work. You do understand that work is force times distance moved, right? Static forces do no work.

Yes, no movement means no work done.

What I am looking to find out is if a ferromagnetic plate is "sucked in" by a magnet, how much kinetic energy is gained. Also, what the minimum thickness of this plate would have to be to take advantage the full force of this magnet.

Use conservation of energy, viz. the work done by the magnet is equal to vertical component of its displacement multiplied by the objects' weight.

korneld said:
Yes, no movement means no work done.

What I am looking to find out is if a ferromagnetic plate is "sucked in" by a magnet, how much kinetic energy is gained. Also, what the minimum thickness of this plate would have to be to take advantage the full force of this magnet.
Unless the plate starts out very close to the magnet, you have to do a complicated integral of F(x)dx. The force ~1/7 (like Van der Waals) at large distance and becomes indep of x when x<<R (for a magnet with end radius R).
You can decide on the miimum thickness of the plate by solving the following
electrostatics problem: Consider two parallel identical uniformly charged
disks of radius R, a distance L apart. When the distance x above one disk is large enough so that you can neglect the charge on the other plate is the same as when the plate is thick enough. The plate thickness L will depend on x, R and what you mean by "full force"

Meir Achuz said:
Unless the plate starts out very close to the magnet, you have to do a complicated integral of F(x)dx. The force ~1/7 (like Van der Waals) at large distance and becomes indep of x when x<<R (for a magnet with end radius R).
You can decide on the miimum thickness of the plate by solving the following
electrostatics problem: Consider two parallel identical uniformly charged
disks of radius R, a distance L apart. When the distance x above one disk is large enough so that you can neglect the charge on the other plate is the same as when the plate is thick enough. The plate thickness L will depend on x, R and what you mean by "full force"

Thanks for the info.

'... and what you mean by "full force"': I've read on one permanent magnet manufacturer's website (which now I can't seem to find) that the material to be attracted by the magnet has to to have a certain thickness, but beyond that point thickness is irrelevant. I am assuming that below it, the magnetic field will have a lesser effect on the material.

## 1. What is work done by a permanent magnet?

The work done by a permanent magnet refers to the energy expended or transferred when the magnet moves or causes motion in another object or system. This work is a result of the magnetic force exerted by the magnet and can be calculated by the product of the force and the distance moved.

## 2. How is work done by a permanent magnet different from work done by other sources?

The work done by a permanent magnet is different from work done by other sources because it is a result of magnetic force, which is a non-contact force. Other sources, such as mechanical work, involve physical contact between objects to transfer energy.

## 3. Can work be done by a permanent magnet in a vacuum?

Yes, work can still be done by a permanent magnet in a vacuum. This is because magnetic force can still act on objects without the presence of air or other medium. The absence of air resistance in a vacuum may even increase the efficiency of the work done by the magnet.

## 4. How does the strength of a permanent magnet affect the work it can do?

The strength of a permanent magnet directly impacts the amount of work it can do. A stronger magnet will exert a greater magnetic force, resulting in more work being done. This is why stronger magnets are often used in applications where more work needs to be done, such as in motors or generators.

## 5. What are some practical applications of the work done by permanent magnets?

The work done by permanent magnets has many practical applications, including in motors, generators, speakers, and magnetic levitation systems. Permanent magnets are also used in medical devices, such as MRI machines, and in everyday objects like credit cards and refrigerator magnets.

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