Magnetic Damping: Solving with Faraday's Law

In summary, the problem involves a bar magnet suspended by two pieces of string and oscillating rotationally. The oscillations are damped by eddy currents induced in an aluminium sheet placed underneath the magnet. The equations for undamped motion have been derived, and considering Faraday's Law and Lenz's Law may help solve the problem. The effects of the eddy currents on the bar magnet should also be taken into account.
  • #1
murdochious
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Homework Statement


I'd really appreciate it if someone could point me in the right direction in terms of equations to use for this problem:
Bar magnet suspended at either end by 2 pieces of string which are attached vertically above the magnet to a stationary metal rod (so that the bar magnet oscillates rotationally), underneath the magnet I placed a sheet of aluminium, so when i rotated the magnet and released it, the oscillations were damped by the eddy current induced in the sheet of aluminium below it. I understand that this is because the eddy current induced in the aluminium has its own magnetic field, and a force acts between this field and the magnetic field of the bar magnet.

Homework Equations


I have already derived equations for undamped motion of the system, and can find the starting energy of the system by either integrating torque with respect to x (x being original angle displace) or by using E=0.5Iw^2 (w=rotational velocity.) The equations for torque (T), acceleration (a) and velocity (w)in terms of x are :
T=-0.1sinx(0.5+0.5cosx)^0.5
a=T/I (I=moment of inertia=1/375 in my set up)
w^2=100(0.5+0.5cosx)^1.5 - 25root2 (25root2 is due to starting angle of pi/2)

I don't think the equations affect the solution to the magnetic problem, I just thought id add them for anyone who is interested.


The Attempt at a Solution


I have found the equations for undamped motion, and understand the principle of the dampening, I considered trying to use faraday's law saying the aluminium sheet could be treated as a one turn coil? but my friend said that was wrong. Presumably the solution will be only solvable if i have equations of motion in terms of time rather than angle displaced, ill work on that.

In terms of explanations- my maths understanding extends to A level Further Pure.
Thanks.
 
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  • #2


Hello, it seems like you are on the right track with considering Faraday's Law. However, treating the aluminium sheet as a one-turn coil may not be the most accurate approach since it is not a complete circuit. You may want to consider using Lenz's Law, which states that the direction of induced current will oppose the change in magnetic flux. In this case, as the bar magnet rotates, the magnetic field passing through the aluminium sheet changes, which induces a current that creates a magnetic field that opposes the bar magnet's field. This creates a force that damps the oscillations.

One way to approach this problem is to calculate the induced current in the aluminium sheet using Faraday's Law, and then use the Lorentz force equation to calculate the force acting on the bar magnet due to the induced current. This force will act in the opposite direction of the bar magnet's motion, causing the oscillations to dampen.

You may also want to consider the effects of the eddy currents on the bar magnet itself. As the bar magnet moves, it will experience a changing magnetic field due to the eddy currents in the aluminium sheet. This may also affect the motion of the bar magnet and should be taken into account in your equations.

I hope this helps guide you in the right direction. Good luck!
 

1. How does magnetic damping work?

Magnetic damping is a process in which the motion of an object is slowed down or brought to a stop by interacting with a magnetic field. This is accomplished by Faraday's Law, which states that a changing magnetic field will induce a current in a conductive material. This induced current creates its own magnetic field, which interacts with the original magnetic field and causes a force that opposes the motion of the object.

2. What are the applications of magnetic damping?

Magnetic damping is commonly used in devices such as compasses, galvanometers, and seismometers to dampen the oscillations and reduce the effects of external disturbances. It is also used in mechanical systems, such as shock absorbers, to decrease the impact of vibrations and ensure smooth motion.

3. What factors affect the strength of magnetic damping?

The strength of magnetic damping depends on several factors, including the strength of the magnetic field, the speed and direction of the object's motion, and the conductivity of the material. A stronger magnetic field or a faster moving object will result in a stronger damping effect. Similarly, a highly conductive material will experience more damping compared to a less conductive material.

4. Can magnetic damping be used to generate electricity?

Yes, magnetic damping can be used to generate electricity through the process of electromagnetic induction. When an object with a conductive material moves through a magnetic field, it creates an induced current. This induced current can be harnessed to generate electricity, as demonstrated by Faraday's Law.

5. What are the limitations of magnetic damping?

One limitation of magnetic damping is that it only works on objects with conductive materials. Materials such as plastic or wood will not experience any magnetic damping. Additionally, the strength of the damping effect decreases as the object moves further away from the magnetic field source. This means that for larger objects or objects with weaker magnetic fields, the damping effect may not be significant enough to slow down the motion.

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