# Force & energy in cutting and stretching magnetic field lines?

• Luke2642
In summary: The flux flows through the steel and holds it with huge force. By turning easily the magnet with a low torque, the flux no longer flows through the sheet of steel, and remains inside the iron keeper sides.
Luke2642
I have an ordinary switchable magnet for holding tools to a lathe. It's like a magnetic force gearbox, but I can't quite understand the force multiplication.

When placed on a steel surface the switch force is approximately ~5N on both finger and thumb at 1.5cm radius acting over a 3cm arc length.
When not on a steel surface, the torque to turn the switch is significantly more, perhaps double.
However, both of these are significantly less than the holding force, which is over 100N.

They're available at 700N and easily operated with your fingers.

https://en.wikipedia.org/wiki/Magnetic_switchable_device

So imagine three scenarios to remove the device from the surface:

a) Leave the switch on. You yank it off, perpendicular, with enormous effort. The switch now feels sprung, feeling like it releases energy as you turn it off. This makes sense.
b) Leave the switch on. Grip it with one hand, and tilt it off at one edge. This is quite easy. Roll over, 90 degrees on it its side. This is very easy. Now lift it away with no effort (except against its weight obviously). Again, turning the switch off now feels like releasing a spring.
c) Switch it off. The switch doesn't feel sprung, it requires a small constant torque. Now lift it away easily. This is very very easy.

My simple brain can comprehend that in a) the holding force is acting over a very short distance and in c) the switch is turned over a long distance, and b) is somewhere in the middle. The total work done should be the same. But I can't understand why 'steering' field lines takes a little force yet 'stretching' them takes so much. I don't understand why b) is so easy either, it doesn't seem to be accounted for by simple mechnical advantage of leverage alone.

Why does 'cutting' magnetic field lines perpendicular to their direction take less foce than 'stretching' them parallel to their direction? Shouldn't the force per unit distance be equal?

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• Switchable magnet.jpg
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Luke2642 said:
Why does 'cutting' magnetic field lines perpendicular to their direction take less foce than 'stretching' them parallel to their direction?

You can't "cut" magnetic field lines. So I don't understand the question.

Fair enough, perhaps that's my bad terminology. You can steer them through a surface that cuts perpendicular through them.

In which case, my questions are: why does it appear to take 10 times less force to switch it off than to lift it perpendicularly from the surface? Why is lifting it onto one edge then rolling it onto the side take so little force, yet pulling it perpendicular so much harder, if the result is the same?

When switched on, the flux flows through the steel and holds it with huge force. By turning easily the magnet with a low torque, the flux no longer flows through the sheet of steel, and remains inside the iron keeper sides.

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• Switchable magnet 3.jpg
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## 1. What is the concept of force and energy in cutting and stretching magnetic field lines?

The concept of force and energy in cutting and stretching magnetic field lines refers to the interaction between a magnetic field and a conductor. When a conductor moves through a magnetic field, the field exerts a force on the conductor, causing it to experience a change in energy.

## 2. How does cutting and stretching magnetic field lines affect the flow of electricity?

Cutting and stretching magnetic field lines can induce an electric current in a conductor. This is known as electromagnetic induction. The changing magnetic field creates an electric field, which in turn causes the flow of electrons in the conductor, resulting in an electric current.

## 3. What factors affect the strength of the force and energy in cutting and stretching magnetic field lines?

The strength of the force and energy in cutting and stretching magnetic field lines depends on the strength of the magnetic field, the speed of the conductor, and the angle between the direction of motion and the magnetic field lines. The greater these factors, the stronger the force and energy will be.

## 4. Can the force and energy in cutting and stretching magnetic field lines be used for practical applications?

Yes, the force and energy in cutting and stretching magnetic field lines have several practical applications. It is the basis of generators and motors, which are used to generate electricity and convert it into mechanical energy. It is also used in devices such as transformers and electric motors.

## 5. How does the direction of the magnetic field affect the force and energy in cutting and stretching magnetic field lines?

The direction of the magnetic field affects the force and energy in cutting and stretching magnetic field lines. If the direction of the magnetic field is perpendicular to the direction of motion of the conductor, the force and energy will be at their maximum. However, if the direction of the magnetic field is parallel to the direction of motion, there will be no force or energy exerted on the conductor.

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