![]() ![]() The above values illustrate a pattern: as the separation distance is doubled, the electrostatic force is decreased by a factor of four. The inverse square relationship between electrostatic force and separation distance is illustrated in the table below. This square effect makes distance of double importance in its impact upon electrostatic force. And if the separation distance is tripled (increased by a factor of 3), then the electrostatic force is decreased by a factor of nine (3 raised to the second power). So if the separation distance is doubled (increased by a factor of 2), then the electrostatic force is decreased by a factor of four (2 raised to the second power). That is, the factor by which the electrostatic force is changed is the inverse of the square of the factor by which the separation distance is changed. Careful observations show that the electrostatic force between two point charges varies inversely with the square of the distance of separation between the two charges. The pattern between electrostatic force and distance can be further characterized as an inverse square relationship. ![]() Electrostatic force and distance are inversely related. In a similar manner, charged balloons are observed to exert their greatest influence upon other charged objects when the separation distance is reduced. Yet if the tube is brought closer, an attractive interaction is observed and the strength is so significant that the paper bits are lifted off the table. The electrical interaction is so small at large distances that the golf tube does not seem to exert an influence upon the paper bits. Consider a charged plastic golf tube being brought near a collection of paper bits at rest upon a table. These observations are commonly made during demonstrations and lab experiments. Electrical forces are extremely sensitive to distance. ![]() And decreasing the separation distance between objects increases the force of attraction or repulsion between the objects. Increasing the separation distance between objects decreases the force of attraction or repulsion between the objects. In electrostatics, the electrical force between two charged objects is inversely related to the distance of separation between the two objects. Inverse relationships are common in nature. This type of cause-effect relationship is described as being an inverse relationship. Observation might also indicate that an increase in one variable always causes another measurable quantity to decrease. This type of cause-effect relationship is described as being a direct relationship. Careful observation and measurement might indicate that a pattern exists in which an increase in one variable always causes another measurable quantity to increase. This search for cause and effect often leads to conclusive evidence that two variables are causally related (or not causally related). How does the distance between two charged objects affect the force of attraction or repulsion that they encounter? How does the frequency of a sound wave affect the speed at which the sound wave moves? How does the distance from a page to a light bulb affect the amount of light that illuminates the paper's surface? How does the speed of a falling object affect the amount of air resistance that it experiences? How does the mass of an object affect its acceleration? The goal is to answer the question of how does a change in a set of variables or conditions causally affect an observable outcome? In Physics, this search for cause and effect leads to questions like: How does a force affect the acceleration of an object? Scientists modify a set of conditions to see if there is a pattern of behavior in another set of measurable quantities. Nature is probed in order to find relationships and mathematical patterns. Cause and effect is the focus of science. Science in general and Physics in particular are concerned with relationships. ![]()
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