ELECTROMAGNETIC
CANNON
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.
Outline
Experimental setup
 Experimental procedure
 Typical result
 Statistics and explanation
 Relative parameters

Experimental Setup
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.

Typical Result
Video
Qualitative Explanation
The “steel” ball is magnetized, with the same
direction as the magnetic field in the solenoid.
Faraday’s Law
Curie’s Law
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
d

F B
dx
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.
d

F B
dx
Parameters
Voltage
 Solenoid

 Length
 Layer
 Diameter
(→Inductance)
Capacitance
 Resistance
(→frequency)

Magnetic field
Ball
Magnetic permeability
Resistance
Mass
Shape
Initial position
Experiment I

Speed vs. Voltage
 Parameter
: Voltage (from 30V ~50V)
 Initial Condition :
 Capacitance:
1470μF
 Number of Layers: 5 layers
 Length: 1.5 cm
 Position of Cannon: In front of the solenoid (0 mm)
 Mass: 0.014 g
Voltage

Speed is positively related to the voltage.
Experiment II

Speed vs. Capacitance
 Parameter
: Capacitance (from 470μF to 3300μF)
 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
Capacitance

A peak occurs at 1470 μF.
Experiment III

Speed vs. Number of Layers
 Parameter
: Number of layers (4~8 layers)
 Initial Condition :
 Voltage:
50 V
 Capacitance: 1470 μF
 Length: 1.5 cm
 Position of Cannon: In front of the solenoid (0 mm)
 Mass: 0.014 g
1.5 cm
1
2
3
4
5
6
7
8
Numbers of Layers

A peak occurs at 5 layers.
Experiment IV

Speed vs. Solenoid length
 Parameter
: Length (1, 1.5, 2, 2.5, 3 cm)
 Initial Condition :
 Voltage:
50 V
 Capacitance: 1470 μF
 Number of Layers: 5 cm
 Position of Cannon: In front of the solenoid (0 mm)
 Mass: 0.014 g
Length

A peak occurs at 1.5 cm.
Experiment V

Speed vs. Position
 Parameter
: Position (0~10 mm)
 Initial Condition :
 Voltage:
50 V
 Capacitance: 3700 μF
 Length: 1.0 cm
 Mass: 0.083 g
Position

Speed reaches maximum when the ball
is at the front of the solenoid.
Summary

The fastest speed we achieve is 31.4 m/s, which
happens under
 V=50
V
 C=1470 μF
 Layers=5
 Solenoid Length=1.5 cm
 Position: At the front
 Ball mass=0.014g
 Material: Iron
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

Thank you!