1. IYPT 2010 Austria, I. R. Iran Reporter: Reza M. Namin 1

2. IYPT 2010 Austria, I. R. Iran The Question Two magnets are arranged on top of each other such that one is fixed and the other can move vertically, Investigate the oscillations of the magnet. 2

3. IYPT 2010 Austria, I. R. Iran Main Approach Basic understandings Force evaluation –Gilbert’s model –Ampere’s model –Experiments and comparison Oscillation investigation –Equations of motion –Numerical solution –Potential energy –Frequency investigation –Experiments and comparison Conclusion 3

4. IYPT 2010 Austria, I. R. Iran Basic understanding Effective forces –Gravity (Attractive) Constant in different distances –Magnetic force (repulsive) Inverse relation with distance Static equilibrium & oscillation 4

5. IYPT 2010 Austria, I. R. Iran Force evaluation Gilbert’s model: –Modeling the magnets as magnetic dipoles h : Thickness of the magnets d : Distance between the magnets 5 h h d

6. IYPT 2010 Austria, I. R. Iran Force evaluation Ampere’s model –Modelling the magnets as solenoids –Magnetic field caused by each part of the current: –Force of a part of a current in a magnetic field: 6 d h h r

7. IYPT 2010 Austria, I. R. Iran Force evaluation Numerical solution ran with C# –Converting the continuous solenoids to discreet parts (Finite-difference approximation) 7 d h h r Choosing the first part on the top magnet Computing and all the fields of all the points on the bottom magnet Calculating the force exerted to the specific point on the top magnet Adding up the forces and moving to the next point on the top magnet

8. IYPT 2010 Austria, I. R. Iran Force evaluation Comparison between the two models for magnetic force 8

9. IYPT 2010 Austria, I. R. Iran Force evaluation Experimental setup 9

10. IYPT 2010 Austria, I. R. Iran Force evaluation Experimental results of magnetic force in different distances 10

11. IYPT 2010 Austria, I. R. Iran Force evaluation Comparison between the theories and experimental results on magnetic force 11

12. IYPT 2010 Austria, I. R. Iran Oscillation investigation The equations of motion Finding the position in time from the forces –Numerical force => Numerical position 12

13. IYPT 2010 Austria, I. R. Iran Oscillation investigation Numerical solution –Euler’s method Using a loop in time 13

14. IYPT 2010 Austria, I. R. Iran Oscillation investigation Potential energy 14

15. IYPT 2010 Austria, I. R. Iran Experiments and Comparison Capturing the frames and finding the distance in time 15

16. IYPT 2010 Austria, I. R. Iran Experiments and comparison 16

17. IYPT 2010 Austria, I. R. Iran Conclusion According to the force evaluation: –Considering the magnets to be solenoids (ampere’s model) will give accurate force relation. –Gilbert's model does not lead to precise results compared to the ampere’s model 17

18. IYPT 2010 Austria, I. R. Iran Conclusion According to the oscillation investigations: –The motion of the magnet has been successfully solved numerically. –The motion has more acceleration in top and less in downside of the movement 18

19. IYPT 2010 Austria, I. R. Iran Conclusion –The motion approaches to simple harmonic motion when amplitude approaches to zero. –The motion approaches to free fall bouncing when amplitude approaches to infinity. 19

20. IYPT 2010 Austria, I. R. Iran Conclusion 20

21. IYPT 2010 Austria, I. R. IranIYPT 2010 Austria, National team of I. R. Iran

22. IYPT 2010 Austria, I. R. Iran Frequency 22