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**1. Gaussian Cannon Georgia Alexander Barnaveli Magnet V**

II III IV V A sequence of identical steel balls includes a strong magnet and lies in a nonmagnetic channel. Another steel ball is rolled towards them and collides with the end ball. The ball at the opposite end of the sequence is ejected at a surprisingly high velocity. Optimize the magnet's position for the greatest effect.

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**Presentation Plan Experiment Gaussian Cannon action principles**

Interaction of magnet and ball “Energy source” Gaussian Cannon optimization Multi-stage Cannon

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Experiment Slow motion shot Video

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**Gaussian Cannon action principles**

Momentum conservation law Potential (magnetic) energy difference of initial and final conditions Initial and final conditions I II I II Potential (magnetic) energy: (1) Ball velocity: (2)

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**Magnet and Ball – Magnetic Dipoles Magnetic field picture**

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Force measurement Our installation Schematic representation

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**Acting Force μ- magnetic permeability of steel**

Interaction force of magnetic dipoles: (z – Distance between centers, Magnet dipole moment: ) Magnetic dipole creates magnetic field in vacuum equal to [1]: Due to magnetic field, magnetic dipoles are induced in balls [1]: μ- magnetic permeability of steel Thus the interaction force of magnet and ball is:

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**Experimental Magnets Magnet length: 2a Dipole moment of magnet:**

Magnetic Field Visualization Single Magnet in Free Space Grade = N52 Diameter = 0.5in Thickness = 0.5in Experimental Magnets Magnet length: 2a Dipole moment of magnet:

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**Energy – Initial Condition**

Magnet I II Steel ball radius: a=0,64 cm Mass: m=8 g Magnetic permeability of steel: μ = 700 » 1 Magnet length: 2a Dipole moment of magnet: Magnetic dipole creates magnetic field in vacuum equal to [1]: (3) Due to magnetic field, magnetic dipoles are induced in balls [1]: (4) Dipole energy in magnetic field: (5)

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**Energy – Initial Condition**

Magnet I II Center of the 1st ball: z=2a Center of the 2nd ball: z=4a Magnetic moment induced in ith ball : Magnetic moments in centers of 1st and 2nd balls are: Magnetic field in centers of 1st and 2nd balls : - Magnetic field in the center of ith ball (5) (6) Using (6) and (7) - magnetic moments induced in balls are: (8) (7) Using (5),(7),(8) - Magnetic energy of initial condition is:

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**Energy – Final Condition**

Magnet Magnetic field in centers of 1st and 2nd balls: Induced magnetic moments in balls: Using (5), (10) and (11) potential (magnetic) energy of final condition is: I II

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**Theoretical estimation of velocity**

Potential (magnetic) energy difference of initial and final conditions: The velocity is calculated using kinetic energy: In our experiments: For single-stage 1+2 balls case:

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**Experimental calculation of velocity**

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**Different number of balls for 1 section**

Video (3-7)

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**Different number of balls for 1 section**

Vmax Maximal velocity is achieved with 1+4 balls Reasons: Energy loss (heat, rotation) Alignment of balls Comparison of Pipe and Rails

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**Multi-sectional installation**

Shot Slow motion shot

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**Velocity for “n” sections**

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**Important Points of construction**

Fixing the magnet to avoid it’s backward movement Alignment of balls strictly along one line In case of multi-stage cannon alignment of magnet poles Using same-size balls and magnet Consideration of using non-magnetic balls behind the magnet Consideration of different masses of the last ball

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**Conclusion The very important points of the construction are:**

We constructed the Gaussian cannon Energy source of cannon - difference of the initial and the final potential energies Interaction of magnet and ball = interaction of magnetic dipoles Optimal configuration of cannon: One ball before magnet, other balls (2 or more) - behind the magnet We calculated the ball velocity for 1+2 ball variant of cannon. Theoretical calculations coincide with experimental results. In one-stage cannon maximal velocity is achieved for 1+4 ball configuration. We considered some features of multi-stage cannon The very important points of the construction are: Fixing magnet to avoid it’s backward movement Alignment of balls strictly along one line Using same-size balls and magnet

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**Thank you for attention!**

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References: Kirk T. McDonald. A Magnetic Linear Accelerator. Joseph Henry Laboratories, Princeton University, Princeton, NJ (March 3, 2003) Christian Ucke, Hans Joachim Schlichting. Die Magnetkanone. Phys. Unserer Zeit. 3/2009 (40). P. 152 ;

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