The Electromagnetic Force: An Equation

Introduction

This lab is to measure the determinant factors of the size of electromagnetic force that affect with electric and magnetic fields. The electromagnetic force is carried by the photon and is responsible for atomic structure, chemical reactions, the attractive and repulsive forces associated with electrical charge and magnetism, and all other electromagnetic phenomena. According to Coulomb’s Law, we know electric charges get Coulomb force in the electric field while current receives another applied force, which is Ampere force when it is in a magnetic field. Overall, electromagnetic force is the force that electric charges and current are acted in the electromagnetic field. Electromagnetic force is one of the four fundamental forces in nature. Currently, people can produce strong electromagnetic fields as well as strong electric current due to advanced engineering technologies. Besides, we can obtain a great deal of electromagnetic forces (electrostatic forces) from it. Additionally, it seems that electromotor is driven by magnetic force and electromagnetic force has some further applications such as electrostatic instruments and dust catcher. Overall, this study plays an important role in both our studies in physics and the development of electromagnetism.

Procedure

In this typical experiment, we used controlling variables method to determine the relationships among how current (I), length of wire (L), and strength of magnetic field (B) affect the size of the electromagnetic force that was exerted on the wire. More precisely, we did three separate experiments to obtain each result by using the same method. Diagram 1 Schematic diagram of the experiment

In terms of the relationship between current and the size of the electromagnetic force, we used a digital ammeter to display these current values while we increased the current by using a regulated power supply to provide different required amounts of current. In the meantime, we kept the other two variables, which are magnetic field strength and the length of wire constant and wrote down the results. Likewise, we switched to another variable B, magnetic field strength and used the same way to measure the relationship between B and FB, the size of the electromagnetic force. The equipment we used to control the variable B is a magnet that is assembled with 6 small removable horseshoe magnets. We increased the strength values gradually and recorded the changes in the size of the force. The strength of this field was measured using a hand held magnetic field probe and meter. For the third variable L, the length of wire, we used several small current loops, with plugs attached, allowing them to be suspended in the magnetic field, perpendicular to that field. Similarly, we added the length and kept the current and magnetic field strength unchanged. Apparent mass increased was measured using the 0.01gram balance. According to Newton’s 3rd Law, when the magnet assembly pushes the current loop up with a force FB, the current loop also pushes the magnets down with the same amount of force. You can see results and observations below.

Results

(a) Magnetic Force on a Wire as a Function of Current in the Wire. Current (I) in A| Apparent Mass Increase in g| Magnetic Force (FB) in N| | 1| 0.22| 0.00216| Length of Wire =4.2cm =—| 2| 0.46| 0.00451| =0.042m| 3| 0.68| 0.00667| Magnetic Field = 55.3mTesla|

4| 0.91| 0.00893| =0.0553Tesla|
5| 1.14| 0.01117| |
6| 1.37| 0.01344| |

Current (I) in A| Apparent Mass Increase in g| Magnetic Force (FB) in N| | 1| 0.22| 0.00216| Length of Wire =4.2cm =—| 2| 0.46| 0.00451| =0.042m| 3| 0.68| 0.00667| Magnetic Field = 55.3mTesla|

4| 0.91| 0.00893| =0.0553Tesla|
5| 1.14| 0.01117| |
6| 1.37| 0.01344| |

(b) Magnetic Force on a Wire as a Function of Wire Length
Length of Wire (L)in m| Apparent Mass Increase in g| Magnetic Force (FB) in N| | 0.012| 0.275| 0.0026978| Current = 5A|
0.022| 0.57| 0.0055917| |
0.032| 0.84| 0.0082404| Magnetic Field = 55.3mTesla= ==-=| 0.042| 1.16| 0.0113796| =0.0553Tesla| 0.064| 1.64| 0.0160884| |
0.084| 2.16| 0.0211896| |

Length of Wire (L)in m| Apparent Mass Increase in g| Magnetic Force (FB) in N| | 0.012| 0.275| 0.0026978| Current = 5A|
0.022| 0.57| 0.0055917| |
0.032| 0.84| 0.0082404| Magnetic Field = 55.3mTesla= ==-=| 0.042| 1.16| 0.0113796| =0.0553Tesla| 0.064| 1.64| 0.0160884| |
0.084| 2.16| 0.0211896| |

(c) Magnetic Force on a Wire as a Function of Magnetic Field Strength Magnetic Field Strength (B) in T| Apparent Mass Increase in g| Magnetic Force (FB) 413in N| | 0.0117| 0.30| 0.00294| Current = 4A|

0.0226| 0.50| 0.00490| |
0.0311| 0.76| 0.00745| Length of Wire = 6.4cm= |
0.0413| 1.02| 0.00996| =0.064m|
0.0478| 1.12| 0.01098| |
0.0553| 1.30| 0.01274| |

Magnetic Field Strength (B) in T| Apparent Mass Increase in g| Magnetic Force (FB) 413in N| | 0.0117| 0.30| 0.00294| Current = 4A|
0.0226| 0.50| 0.00490| |
0.0311| 0.76| 0.00745| Length of Wire = 6.4cm= |
0.0413| 1.02| 0.00996| =0.064m|
0.0478| 1.12| 0.01098| |
0.0553| 1.30| 0.01274| |

Analysis

Figure 1 Magnetic Force vs. Current
As we see in the gigure1 that is plotted in terms of the first table in Results, it is easy to determine that magnetic force increase as current increased. And the shape of the graph looks like a linear with a slope of 0.0022. Hence, the relationship between electromagnetic force and current is that electromagnetic force depends directly on the current. In other words, .

Figure 2 Magnetic Force vs. Length of Wire
According to the graph which is plotted based on the second table in Results, we can aware of the consequence – electromagnetic force increased as length of the wire increased. It means the longer the wire is, the stronger the electromagnetic force is. Therefore, the relationship between electromagnetic and the length of the wire is that electromagnetic force depends directly on the length of the wire. The equation is

Figure 3 Magnetic Force vs. Magnetic Field Strength
On the basis of Figure 3 above, we can still obtain the same result – electromagnetic force increased as magnetic field strength increased. As a matter of fact, electromagnetic force is directly proportional to magnetic field strength. The equation is .

Figure 4 Data comparison
In sum, every factor is directly proportional to the size of electromagnetic force, so if we multiply all the three factors together, the product will still directly proportional to the size of electromagnetic force. As we see in Figure 4, the expected values of magnetic force and the results we got are really close to each other. It strongly proves my opinion-the size of electromagnetic force equals to the product of current, length of wire and magnetic field strength. Some errors appeared since the some graphs do not look like a perfect linear. It is because taking off the removable horseshoe magnets in turn changed the magnetic field strength, then the magnetic assembly would be moved around, which might cause the deviation. Overall, the final equation for the relationship among and the other three variables is . Application

An electric motor is an electromechanical device that can convert electrical energy into mechanical energy. Most electric motors work through the interaction of magnetic fields and current-carrying conductors to generate force. Undoubtedly, an electric motor can produce electromagnetic force due to its principles. There are different types of electric motors such as direct current motors and alternating current motors. Most importantly, the operating principle of electric motors is Electromagnetic Induction, which is a phenomenon to convert electrical energy into mechanical energy. Oersted discovered that if there was current going though a conductor, it would produce a magnetic field around the conductor, which could make a compass needle to move. Based on his discovery, Faraday made an experiment to prove if a magnetic field could cause a current-carrying conductor to move. Finally, he discovered the Electromagnetic Induction.
Figure 5 A DC motor

Figure 6 Modern Electric Motor
As we see in the figure, there is a completed circuit and the north pole of the coil points upwards owing to right hand rule. Hence, the armature is forced to rotate due to the magnetic force around it. After a 90-degree rotation, the brushes will be separated from the commentator, causing the disconnection of the circuit. However, the armature will rotate continuously because of inertia and will become vertical. As a result, the circuit will be connected again and the whole process will keep going automatically. Regardless of its cost and actual use, electric motor is the cornerstone of the development of electricity.

The purpose of this experiment is to determine the equation in order to quantize the electromagnetic force related to the magnitude of current, the length of wire and magnetic field strength. The equation is . Also, this investigation improves our experimental skills and the understanding of controlling variables method.