The document summarizes an experiment that investigates the relationship between the separation distance of two magnets and the repelling force between them. It is hypothesized that as the separation distance decreases, the repelling force will increase. The experiment measures the distance a cart travels as it is repelled by one magnet from another at various separation distances. The results show an inverse relationship between separation distance and repelling distance, supporting the hypothesis. In conclusion, the separation distance and repelling force between two magnets have an inverse relationship, where decreasing the separation distance increases the repelling force.

1. Rie Yamada<br />Physics (period 3)<br />March 1, 2011<br />Force of Magnetic Field<br />Introduction<br />In this research, the relationship between a separation of two magnets and a repelling force are investigated by analyzing the distance travelled by a cart with one magnet while the other magnet is placed on a wall, which repels to the magnet on the cart, creating a repelling force. <br />A permanent magnet is an object made from a material that is magnetized and creates its own persistent magnetic field. A magnetic field is an invisible field which exerts magnetic force on substances which are sensitive to magnetism and is responsible for the most notable property of a magnet: a force that pulls on other ferromagnetic materials, such as iron, cobalt and nickel, and attracts or repels other magnets. These elements can be attracted to magnets because of an unpaired electron in the element's outer orbits. These electrons tend to align with magnetic fields, which when spread throughout an entire piece of metal cause the metal to pull toward the magnet, as if it were a magnet itself. Magnets themselves also have this unpaired electron---its alignment is simply frozen in a particular direction rather than responding to the field of another magnet. Any of the elements that are attracted to magnets can actually become temporary magnets, if exposed to magnetic force long enough. This is because being exposed to magnetic force aligns electron spin in a certain direction. When this happens, a north and a south pole are created at the side toward which the electrons point and the opposite of this side; because of the alignment of the electrons, these two points are the most powerful points in the magnet. <br />Figure 1: Separation of magnets and their repelling force<br />(cited from: http://beltoforion.de/magnetic_pendulum/magnetic_pendulum_en.html)<br />When the same poles of two magnets are pressed against each other, there is a repellent force driving the two magnets apart. The alignment of the magnet creates a magnetic field with a north and south pole: north poles are attracted to south poles, but like poles repel. Two north poles or two south poles will invariably push against each other. So the very force that causes magnets to be attracted also causes like magnets to push against each other. This repelling force increase as the distance between the two magnets decreases as demonstrated by Figure 1 above. This can be explained by the equation shown below.<br />The force between two magnetic poles is given by <br /> [equation 1]<br />where<br />F is force or a repelling force<br />qm1 and qm2 are the magnitudes of magnetic poles <br />μ is the permeability of the intervening medium<br />r is the separation or the distance between two magnetic poles<br />As the equation illustrates, when the separation of two magnetic poles decreases, the repelling force created by two magnets increases or vice versa. <br />Moreover, in Newton's Second Law of Motion, he states that force equals mass times acceleration (F=ma). This equation shows that the acceleration of a body is directly proportional to the net unbalanced force and inversely proportional to the body’s mass. When one of the two magnets is placed on a cart and the cart travels as the two magnets repel each other, a change in the distance between two magnets and a change in repelling force affect the distance travelled by the cart because acceleration is an increase the magnitude of the velocity of a moving body and it allows the body to travel a greater distance in time. The increase in the repelling force created by two magnets results in an increase in the distance travelled. <br />As previously stated in equation 1, the repelling force and the distance between magnets are inversely related and the force increases when the distance gets shorter. Also as the second equation F=ma states, the force and acceleration are directly proportional and the acceleration of a cart increases when the repelling force increases. The distance between two magnets affect the repelling force created which then influences the acceleration and the distance travelled by a cart. Thus, the distance between two magnets and the distance travelled by a cart are related to each other: the travelling distance increases as the separation of magnets becomes smaller and vice versa. Based on these theories, it is predicted that the distance between two magnets and repelling force created by them have an inverse relationship. <br />Procedure<br />Figure 2: Procedure of the investigation<br />Distance travelledDistance between two magnetsWallCartMagnet<br />In the experiment, the relationship between a separation of two magnets and a repelling force are investigated. A cart with one magnet attached to it travels when its magnet repels the other magnet which is placed on a wall, creating a repelling force. The distance between two magnets is changed and the repelling force created by them is analyzed, but several factors need to remain unchanged in order to see the relationship between separation of magnets and a repelling force. These controlled factors are the magnitude of two magnets, the mass of a cart, and the friction which affects a cart when it travels. The magnitude of two magnets needs to be kept the same for the investigation because it influences the strength of a repelling force as shown in equation 1. So the same magnets are expected to be used in the entire investigation. The mass of a cart also needs to be kept unchanged the mass of a cart affects the acceleration rate of a cart which travels as shown in the second equation F=ma. The same cart is used for the entire investigation. In addition, the friction, which affects a cart when it travels, also has to be kept stable. This can be achieved by using the same cart and allowing the cart to travel on the same floor. In the investigation, the distance between two magnets varies from 0cm to 9cm with six different lengths and the distance travelled by a cart is measured in centimeters to figure out the effect of separation of magnets on their repelling force. Three trials in total are held and their averages are calculated.<br />Data Collection and Processing<br />Distance between magnets(±0.1cm)Repelling distance(±1.0cm)Trial 1Trial 2Trial 3Average9.03.33.43.83.57.06.16.56.66.45.08.88.69.58.93.011.612.012.111.91.038.838.936.438.00.0108.1108.7109.2108.7<br />Table 1: This table shows the relationship between the distance between two magnets and the repelling distance travelled by a cart. For each distance, three trials are held and their average is calculated. No numbers are perfectly accurate so the uncertainty is shown for each value. The largest average deviation of the trials (1.0cm) is used as the uncertainty of the average repelling distance. <br />Figure 3: This figure shows the relationship between the distance between two magnets and the repelling distance travelled by a cart when the two magnets repel each other. As the graph is downward sloping, the distance between magnets and the repelling distance are inversely related. When the distance between magnets increase, the repelling distance travelled by the cart decreases. As the line fits within the uncertainty bars for all values except the first one, so the data are pretty accurate. The reason why the first one does not fit to the curve is that although it says that the distance between two magnets is zero centimeter, it is not possible to have zero distance as two magnets repel each other and do not touch each other. Thus, the first point may shift to right as the distance may be greater than zero and it gets closer to the curve. <br />Conclusion<br />The main purpose of the investigation was to find the relationship between the separation of magnets and their repelling force. In order to analyze their relationship, the relationship between the separation of magnets and the repelling distance travelled by a cart when two magnets repel each other was analyzed first, as the repelling distance can represent the strength of the repelling force. It was predicted that the separation of magnets and the repelling force have an inverse relationship. Throughout the investigation, the prediction to the research question was supported. As figure 3 demonstrates that the distance between two magnets has an inverse relationship with the repelling distance, the repelling distance increases when the magnets get closer. Therefore, the result of the investigation demonstrates that the separation of magnets and the repelling distance travelled by the cart when two magnets repel each other have the inverse relationship: the closer the two magnets are, the greater distance the cart travels. From this conclusion, it also can be implied that the separation of magnets and the repelling force have the inverse relationship as well because the repelling distance is used to represent the repelling force created by two magnets. Thus, the closer the two magnets are, the greater the repelling force is. The reason why the repelling force increases when two magnets get closer is that the two magnets create their own magnetic fields and these magnetic fields have weaker force on an object if the object gets further away from them. As the like poles of the two magnets get closer to the other, their magnetic fields create stronger repelling forces on each other and thus the cart can travel a longer distance. <br />All numbers and values shown in the data are always not perfectly accurate and there are uncertainties such as 1.0cm for the repelling distance (shown in table 1) so the data is not considered perfectly applicable. Since figure 3 shows that each point fits the curve within its uncertainty, it can be said that the data taken in the investigation is accurate enough to drag a conclusion. Also, the data and the conclusion drawn from the data agree with the theories previously mentioned in the introduction so it can be said that the investigation was successful. But the level of confidence in conclusion is not very high because the level of uncertainty is high as it is actually greater than one and it implies that the quality of the data is not very well. In addition, it is also significant to mention that although it is good to make the data fit to a linear line in order to prove that the distance between magnets and repelling distance are inversely proportional, we chose not to do that because our data did not fit a linear line when x was converted to 1/x. Therefore, figure 3 successfully shows that the two variables have an inverse relationship as one increases when the other decreases, but the data could not show whether or not these two variables have a direct inverse relationship. <br />The result of this investigation is applicable to any materials which can create a magnetic field. As the conclusion shows that repelling force of two magnetic fields increases when these magnetic fields get closer, any materials which create magnetic fields would show the relationship of distance and repelling force similar to that shown in the investigation. The very first idea for this investigation was to use solenoid in order to find the relationship between distance of two magnetic fields and their repelling force. However, solenoids are not suitable materials for the experiment because they are not strong enough to create great repelling force. If solenoids are big and strong enough to create strong magnetic fields, this type of investigation can be applied and similar conclusion would be drawn from its data. <br />Evaluation<br />One of the weaknesses in the investigation is that the cart is pretty old and it did not move smoothly. The data show a small uncertainty and it can be said that the data taken in the investigation are pretty accurate. However, the cart sometimes moved smoothly and sometimes did not move much and the data need to be taken several times and some very different data are rejected to make sure that the data do not have a really large uncertainty. For example, when the distance between the two magnets is 1.0cm, the data show the average of 38.0cm and the three trials showed 38.8cm, 38.9cm, and 36.4cm. But four trials actually have been held because in one trial, the distance travelled by the cart was only 20.3cm as the cart could not move smoothly. In order to improve the reliability of data, any tools used in an investigation need to be checked before the investigation and it is significant to make sure that all tools work well. <br />Moreover, as previously explained in figure 3, although it is assumed that the distance between two magnets is zero, the distance is not actually zero because two magnets repel the other and do not touch each other, creating a very small gap between them. This inaccuracy in the data is demonstrated in figure 4 as well. Figure 4 successfully illustrates that the repelling distance travelled by the cart decreases when the distance between two magnets increase as most of the points fit the curve within their uncertainties. However, the one point for the zero distance between two magnets does not fit the curve as it is not possible to have zero distance as two magnets repel each other and do not touch each other. Thus, the point for the zero distance between magnets is expected to shift to the right as the distance may be greater than zero and it can get closer to the curve. This weakness shows the importance of measuring each value as accurately and carefully as possible so that the data can be trusted. <br />