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

Bdx

dF

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.

Bdx

dF

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 2 3 4 5 6 7 81.5 cm

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!