Prove or conversely disprove the inverse square law.

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Adam Hodgkinson

Introduction

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 ¼.    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 ∕ 4πr2

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,

4πGM = Intensity at the surface of sphere of influence.

4πr2

Where G is the gravitational constant, M the mass of the object, and r the distance from the centre point.     By cancelling out the 4π 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

 4πr2

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

4πε0 r2

Where Q/ε0  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.                                          

Sources - Advanced physics by Wendy brown, Terry Emery, Martin Gregory, Roger

                 Hackett, Colin Yates

-  Physics for you By Keith Johnson, Simmone Hewett, Sue Holt, John Miller

Hypothesis

I believe that both gamma sources and Light sources, the point sources I plan to investigate will adhere to the inverse square law.     In this I feel that when intensity is plotted against distance, a curve will be described.     If the reciprocal of the square root of the count is plotted against the distance I feel a straight line will be described.

Trial experiment

I have done two forms of trial experiment to determine, which wave is best to investigate the inverse square law and which equipment is best suited for experimental work.    There are 4 main areas to which the inverse square law applies these are, Gravity, sound, electric fields, and members of the electro-magnetic spectrum.    To investigate gravity is impractical as you can do 1 of three things, you will have to work over enormous distances, I.E. several astronomical units, or have instrumentation accurate enough to measure the gravitational attraction of tiny measures, or do a completely theoretical experiment.   All of these options are impractical.    It is impractical to investigate electric fields on a safety aspect, you will either need extremely sensitive equipment to detect a field, which is weak enough to safely work in, or risk serious injury and work with a very powerful electric field.    Both of these are impractical.    It is possible to investigate sound, but in my experience unless your equipment is extremely sensitive, and not at my disposal, it simply doesn’t work.    So I chose to investigate two members of the electro-magnetic spectrum, Gamma radiation and visible light.   Ideally I would have investigated gamma radiation and radio waves, the two opposing ends of the spectrum, however we do not have the equipment available to measure radio waves with wavelengths in the region of 103 meters, so I did experiments involving visible light and Gamma radiation.   Both members of the electro-magnetic spectrum, gamma being present at the far end of the spectrum with extremely high frequency of anything from 1019 to 1021 Hz and a low wavelength of anything from 10-11 to 10-13 metres.   It is Gammas high frequency, which gives it a high energy level; this is because the energy of a member of an electromagnetic wave is deduced by multiplying the frequency by planks constant. Visible light is present on the right side, with relatively low energies.    It has a wavelength of 10-6 meters and a frequency of 1015 Hz.  

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Both experiments were essentially the same, move a detector away from a source of waves, and measure the intensity of the wave at certain distances, in order to determine if the intensity drops of inversely proportional to the square of the distance.  

Prior to beginning the Gamma experiment using the rad count I took background counts over a period of a minute, then waited a minute, then took it again over the same time period of 1 minute.  I did this at a variety of places in the lab I was using to find if there ...

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