1. ELECTROMAGNETIC CANNON

2. Question  A solenoid can be used to fire a small ball. A capacitor is used to energize the solenoid coil. Build a device with a capacitor charged to a maximum 50V.  Investigate the relevant parameters and maximize the speed of the ball.

3. Outline  Experimental setup  Experimental procedure  Typical result  Statistics and explanation  Relative parameters

4. Experimental Setup

5. Electro circuits & Capacitors Solenoid & Muzzle

6. Experimental Setup Solenoids of different lengths and layers Balls of different sizes, mass and shapes

7. Experimental Setup (Inductance) 0.5 cm 67 8 9 Layers 0.05 0.10 0.15 0.20 1.0 cm 1 2 3 4 5 678 0.007 0.03 0.06 0.12 0.17 0.34 0.33

8. Experimental Setup (Inductance) 1 2 3 4 5 6 7 8 1.5 cm 0.01 0.04 0.100.140.280.33 0.60 0.63 1 2 3 4 5 6 7 8 2 cm 0.02 0.07 0.150.210.430.49 0.87 1.13

9. Experimental Setup (Inductance) 1 23 4 3 cm 0.45 0.240.110.03 1 2 3 4 2.5 cm 0.02 0.37 0.210.08

10. Experimental Procedure  Charge the capacitor five times longer than its time constant.  Connect the capacitor to the solenoid.  Measure the distance the bar flies to estimate the initial speed.  Repeat the procedure above.

11. Typical Result Video

12. Typical Result  Eliminate the data with significant deviation.

13. Qualitative Explanation  The “steel” ball is magnetized, with the same direction as the magnetic field in the solenoid.  Faraday’s Law  Curie’s Law

14. Why It Moves  A magnetic dipole in magnetic field tends to move toward where the magnetic potential is less (i.e. the middle of the solenoid) ‏  Magnetic domain model  Loop model

15. How Fast It Moves  The magnetic field is associated with the discharging process of the capacitor, and the position of the ball.  The dipole moment is associated with the changing rate of the magnetic field, and the magnetization of the ball.

16. Parameters  Voltage  Solenoid  Length  Layer  Diameter (→ Inductance)  Capacitance  Resistance ( → frequency) ‏  Magnetic field  Ball  Magnetic permeability  Resistance  Mass  Shape  Initial position

17. Experiment I  Speed vs. Voltage  Parameter : Voltage (from 30V ~50V) ‏  Initial Condition : Capacitance: 1470 μ F Number of Layers: 5 layers Length: 1.5 cm Position of Cannon: In front of the solenoid (0 mm) ‏ Mass: 0.014 g

18. Voltage  Speed is positively related to the voltage.

19. Experiment II  Speed vs. Capacitance  Parameter : Capacitance (from 470 μ F to 3300 μ F) ‏  Initial Condition : Voltage: 50 V Number of Layers: 5 layers Length: 1.5 cm Position of Cannon: In front of the solenoid (0 mm) ‏ Mass: 0.014 g

20. Capacitance  A peak occurs at 1470 μ F.

21. Experiment III  Speed vs. Number of Layers  Parameter : Number of layers (4~8 layers) ‏  Initial Condition : Voltage: 50 V Capacitance: 1470 μ F Length: 1.5 cm Position of Cannon: In front of the solenoid (0 mm) ‏ Mass: 0.014 g 1 2 3 4 5 6 7 8 1.5 cm

22. Numbers of Layers  A peak occurs at 5 layers.

23. Experiment IV  Speed vs. Solenoid length  Parameter : Length (1, 1.5, 2, 2.5, 3 cm) ‏  Initial Condition : Voltage: 50 V Capacitance: 1470 μ F Number of Layers: 5 cm Position of Cannon: In front of the solenoid (0 mm) ‏ Mass: 0.014 g

24. Length  A peak occurs at 1.5 cm.

25. Experiment V  Speed vs. Position  Parameter : Position (0~10 mm) ‏  Initial Condition : Voltage: 50 V Capacitance: 3700 μ F Length: 1.0 cm Mass: 0.083 g

26. Position  Speed reaches maximum when the ball is at the front of the solenoid.

27. Experiment VI  Speed vs. Mass  Parameter : Mass (0.014,0.083, 0.19 g) ‏  Initial Condition : Voltage: 50 V Capacitance: 1470 μ F Number of Layers: 5 cm Length: 1.5 cm Position of Cannon: In front of the solenoid (0 mm) ‏

28. Mass  Faster when the projectile is lighter.

29. Experiment VII  Speed vs. Material  Parameter : Material (iron, cobalt, nickel, copper) ‏  Initial Condition : Voltage: 50 V Capacitance: 1470 μ F Number of Layers: 5 cm Length: 1.5 cm Position of Cannon: In front of the solenoid (0 mm) ‏

30. Material  As a good ferromagnetic material, iron flies faster than any other ones.

31. Summary  The fastest speed we achieve is 31.4 m/s, which happens under  V=50 V  C=1470 μ F  Layers=5  Solenoid Length=1.5 cm  Position: At the front  Ball mass=0.014g  Material: Iron

32. Summary  In this case, energy stored in the capacitor is 1.84 J.  Energy transferred to the projectile is 6.91*10 -3 J.  Ratio=3.76*10 -3

33. Thank you!