Calculating Conservation of Energy for Magnet Dropping Through Coil

In summary, the effect of dropping a magnet through a single coil of wire can be understood by considering the forces acting on the magnet, the principles of electromagnetism, and the conservation of energy. To solve for the velocity of the magnet at the end of the coil, it is necessary to consider the changing velocity of the magnet and the changing induced current in the wire. This can be done through experimentation or by setting up a differential equation that takes into account these factors. Keep exploring and experimenting to find the best solution for your problem.
  • #1
Redro
1
0
Hi

I am trying to understand the effect of dropping a magnet through a single coil of wire. If there is one turn of wire, connected to a resistor, and a magnet with known mass and flux density is dropped vertically through the coil, a current will be induced in the coil. The forces acting on the magnet will be gravity, and a magnetic force. This force will be proportional to the current induced in the coil, such that

F = NBI*pi*(coil diameter)
where
N = number of coils
B = flux density

Lenz's law will also apply, giving the induced voltage as a function of the change of flux per unit time.

So, if a magnet is dropped from a known height above the coil, it will have a known potential energy. The motion through the coil will induce a current in the wire that will be dissipated as heat in the resistor. Using the conservation of energy principle, the kinetic energy and the dissipated energy will equal the initial potential energy (assuming the reference point is at the base of the coil, therefore potential energy at the final position can be ignored).

When I try to calculate the velocity of magnet at the end of the coil I end up with two unknown variables, the current and the velocity.

This seems like it should be a simple case of conservation of energy but it only seems solvable if one of these variables is held constant eg. the current. I can then solve it incrementally in excel. This is not an adequate solution to the problem as I believe it should be possible to solve it using the eqations above and the standard equations of motion using Newton's Second Law and a summation of the forces acting on the magnet.

Any ideas will be welcome.

Thanks
 
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  • #2
for your post. It seems like you have a good understanding of the principles involved in this scenario. To answer your question about solving for the velocity of the magnet at the end of the coil, it is important to consider the factors that affect the induced current in the wire.

Firstly, the rate of change of flux through the coil will depend on the speed of the magnet as it passes through the coil. This means that the velocity of the magnet is not a constant, but will change as it moves through the coil. Secondly, the number of turns in the coil and the strength of the magnetic field will also affect the induced current.

To solve for the velocity of the magnet at the end of the coil, you will need to consider the motion of the magnet through the coil and how it affects the induced current. This can be done by using the equations you mentioned, along with the equations of motion and the principles of electromagnetism.

One approach could be to set up a differential equation that takes into account the changing velocity of the magnet and the changing current in the coil. This would require some simplifications and assumptions, but it could provide a more accurate solution than using a constant current.

Another approach could be to use experimental data to determine the relationship between the velocity of the magnet and the induced current, and then use that relationship to solve for the velocity at the end of the coil.

I hope this helps you in your research. Keep exploring and experimenting to find the best solution for your problem. Good luck!
 

Related to Calculating Conservation of Energy for Magnet Dropping Through Coil

What is conservation of energy?

Conservation of energy is a fundamental principle in physics that states that energy cannot be created or destroyed, it can only be transformed from one form to another.

How is conservation of energy applied to a magnet dropping through a coil?

When a magnet is dropped through a coil, it experiences a change in potential energy as it moves closer to the coil. This potential energy is then converted into kinetic energy as the magnet accelerates towards the coil. As the magnet passes through the coil, it induces an electric current which in turn creates a magnetic field. This magnetic field produces a force that opposes the motion of the magnet, converting its kinetic energy back into potential energy. This process continues until the magnet comes to a stop at the bottom of the coil, with all of its potential energy converted back into kinetic energy.

What factors affect the conservation of energy in this scenario?

The main factors that affect the conservation of energy in this scenario are the strength of the magnetic field, the mass of the magnet, the distance between the magnet and the coil, and the resistance of the coil. These factors can impact the amount of potential and kinetic energy involved in the system, and therefore affect the conservation of energy.

Are there any limitations to the conservation of energy principle in this situation?

As with any principle in physics, there are some limitations to the conservation of energy in this situation. For example, the conservation of energy principle assumes that there is no external force acting on the system. In reality, there may be some small external forces, such as air resistance, that can affect the energy transformation process. Additionally, the principle assumes that all energy transformations are perfectly efficient, which may not always be the case in real-world scenarios.

How can the conservation of energy be calculated in this scenario?

The conservation of energy can be calculated by considering the initial potential energy of the magnet, the kinetic energy as it falls towards the coil, and the final potential energy at the bottom of the coil. By using equations for potential and kinetic energy, the total energy before and after the magnet drops through the coil can be compared to ensure that energy is conserved.

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