Prove or conversely disprove the inverse square law Essay

My aim of this experiment is to prove or conversely disprove the inverse square law, which simply states that the intensity of any point source, which spreads its influence equally in all directions without a limit to its range, will decrease in intensity inversely proportional to the square of the distance. Background information Research As first proposed by Isaac Newton when proposing his universal law of gravitation it became clear to him that the intensity of gravity would decrease according to the inverse of the square of the distance. This is the heart of the inverse square, which states for any point source, which spreads its influence equally in all directions without a limit to its range, will obey the inverse square law. Quite simply the inverse square law states that for sources emitted from a point the intensity will be deduced as the inverse of the square of the distance. You double the distance you reduce the intensity by a factor of 1/4. This has applications in electric fields, light, sound, gamma radiation, and gravity. All of these are expressed in the medium of a field. To explain the properties involved in a field it is useful to use the idea of flux. When water flows form a ‘source’ to a sink it is transferred at a certain rate, or flux. The flux density will be the mass of water per second crossing a unit area perpendicular to the flow. We can think of energy density in a similar way. Energy flux density is normally referred to as intensity. Field strength and energy flux density are related. The strength of a field will fall off proportionally. The idea of flux can be applied to fields in which there is no obvious evidence for anything actually being transferred, such as static electrical fields, gravitational fields and magnetic fields. The mathematics that model flux are the same whatever the field. Generally this can be summed up in a formula which states the intensity at a point on a sphere of influence will be deduced by the source strength divided by 4 times pi times the radius squared, where this is the surface area over which the initial source has spread it’s influence. I = S / 4? r2 This formula manifests itself in a variety of ways when put into context. When applied to gravity the formula to show the acceleration due to gravity at the surface of a body is, 4? GM = Intensity at the surface of sphere of influence. Where G is the gravitational constant, M the mass of the object, and r the distance from the centre point. By cancelling out the 4? section we are left with the more elegant formula, GM = acceleration due to gravity r2 Where acceleration due to gravity would be equivalent to the intensity of the source. As the distance is doubled, the intensity is reduced by a factor of 4. So theoretically gravity obeys the inverse square law. When applied to sound we get the formula, P = I 4? r2 Where P is the source power, I the intensity at surface of sphere, and r the distance from the source power. So again we see that as we double the distance we reduce the intensity by a factor of 4. The differce here that as sound is not of ethereal nature it is affected by its surroundings and only works without reflections, or reverberations. The behaviour of point charges in an electrostatic field will obey coulombs law, which in turn obeys the inverse square law. The formula here is, Q = E 4 0 r2 Where Q/? 0 is the source strength, E is the strength of the electrostatic field, and r is the distance. So again we see that as the distance is doubled, the intensity of the field is reduced by a factor of four.