# Calculating Force Between a Solenoid and a Cylindrical Magnet

• abdo799
In summary, the conversation discusses the difficulty of calculating the opposing force experienced by a magnet moving towards a solenoid, with the speaker searching for resources on how to make these calculations. It is noted that there is no closed-form analytical solution and the force must be calculated numerically. The conversation also mentions a link to similar problems and the importance of considering factors such as the dynamics and resistance in these calculations.
abdo799
I've read a lot and watched a lot about lenz's law , about how a magnet moving towards a solenoid will experience an opposing force. But I tried to search how to calculate this force , found nothing .
So i tried to find how to calculate force between 2 magnets . Found on wikipedia how to calculate force between 2 magnetized areas, 2 cylindrical magnets and 2 dipoles ( very basic , resembling coulombs law). So , which one should i use when calculating force between solenoid and the cylindrical magnet moving towards it ?

I assume you are speaking of a shorted solenoid? If yes, then the answer is neither because this is not a magnetostatics question. The opposing force depends on the dynamics--the relative speed of magnet and solenoid, the rate of change of magnetic flux in the solenoid, and the R/L time constant of the solenoid. These are more complicated calculations than your statics case.

marcusl said:
I assume you are speaking of a shorted solenoid? If yes, then the answer is neither because this is not a magnetostatics question. The opposing force depends on the dynamics--the relative speed of magnet and solenoid, the rate of change of magnetic flux in the solenoid, and the R/L time constant of the solenoid. These are more complicated calculations than your statics case.

Lets say it's a wire loop , is there a webpage or a book where i can find those calculations?

I took a quick look at webpages and didn't find this problem worked out. It's not simple due to the difficulty of finding the inhomogenous field from a bar magnet and integrating it to find the flux in the loop as the magnet approaches. You will end up solving it numerically (e.g., Matlab).

This link solves similar problems and shows how force depends on motion for a simpler geometry:
One of the problems asks for qualitative solutions to your scenario--but as I indicated, there is no closed-form analytical solution.

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1 person
marcusl said:
I took a quick look at webpages and didn't find this problem worked out. It's not simple due to the difficulty of finding the inhomogenous field from a bar magnet and integrating it to find the flux in the loop as the magnet approaches. You will end up solving it numerically (e.g., Matlab).

This link solves similar problems and shows how force depends on motion for a simpler geometry:
One of the problems asks for qualitative solutions to your scenario--but as I indicated, there is no closed-form analytical solution.
the link doesn't work, is there another one ?
So you're saying that i won't find those calculation because they are so complicated?

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abdo799 said:
the link doesn't work, is there another one ?

Hmm. Try cutting and pasting the following line into Google

Course notes: Faraday's law of induction- mit ocw

The first link listed should be the one.
abdo799 said:
So you're saying that i won't find those calculation because they are so complicated?
Yes. It has no closed form solution, so you'll need to simulate the answer numerically. Solutions to problems with simpler geometry (typically involving a uniform magnetic field) can be written down analytically.

quoting from notes 21 :" Therefore, as the bar magnet approaches the loop, it experiences a repulsive force due to the induced emf. Since like poles repel, the loop must behave as
if it were a bar magnet with its north pole pointing up"
Can we calculate the opposing force at a certain moment?

The static repulsive force between two identical bar magnets will be an overestimate of the actual force. By how much depends on the situation. It becomes a good approximation when
a) the loop is close to the magnet so it intersects much of the magnet's flux
b) the wire loop has no resistance

## 1. What is Lenz's Law?

Lenz's Law is a fundamental principle of electromagnetism that states that the direction of an induced current in a conductor will be in such a way as to oppose the change that caused it.

## 2. How does Lenz's Law relate to magnetic force?

Lenz's Law is closely related to magnetic force because it explains the direction of the induced current in a conductor when it is subjected to a changing magnetic field. The law states that the induced current will flow in a direction that opposes the change in the magnetic field, thus creating a force that opposes the original change.

## 3. Can Lenz's Law be applied to all types of magnetic fields?

Yes, Lenz's Law is a universal principle that applies to all types of magnetic fields, including static, alternating, and rotating magnetic fields.

## 4. How is Lenz's Law used in practical applications?

Lenz's Law has many practical applications, particularly in the design of electric motors and generators. By understanding the direction of the induced current, engineers can design more efficient and effective machines that utilize magnetic fields.

## 5. Is Lenz's Law always true?

Yes, Lenz's Law is always true and has been experimentally verified numerous times. It is a fundamental law of nature that governs the behavior of electromagnetic fields and their interactions with conductors.

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