What is Inverse square law: Definition and 104 Discussions

In science, an inverse-square law is any scientific law stating that a specified physical quantity is inversely proportional to the square of the distance from the source of that physical quantity. The fundamental cause for this can be understood as geometric dilution corresponding to point-source radiation into three-dimensional space.
Radar energy expands during both the signal transmission and the reflected return, so the inverse square for both paths means that the radar will receive energy according to the inverse fourth power of the range.
To prevent dilution of energy while propagating a signal, certain methods can be used such as a waveguide, which acts like a canal does for water, or how a gun barrel restricts hot gas expansion to one dimension in order to prevent loss of energy transfer to a bullet.

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  1. giodude

    I Electricity and Magnetism: Verifying the Inverse Square Law

    Hello, I'm currently working through Purcell and Morin, Electricity and Magnetism textbook and came across a problem in which the goal is to verify the inverse square law. I'm worked through and completed the problem. However, I'm confused how this verifies the inverse square law, I'm posting...
  2. N

    I Sound pressure and inverse distance law

    Hello, I am confused as to how to think about sound pressure and the distance from a sound source. Let's assume that a sound wave is omnidirectional and propagating away from a source in a sphere. We have the following two equations: Pressure = Force/Area Intensity = Power/Area Many texts...
  3. S

    B Does the inverse square law equalize gravity at different spots?

    Inverse square law would reduce the gravity from the parts of Earth that are farthest from our feet. It'll also reduce the gravity from Earth's center by a lesser amount, but would that be lesser enough so the gravity 20 kilometers under our feet is stronger than the core's gravity or even the...
  4. M

    B Proof of inverse square law for gravitation?

    Newton arrived at "there is a force that drives a planet around the star by examining kepler's laws but how did he arrive to inverse square law by kepler's third law (##T^2=\frac {4\pi r^3}{GM}##)? Thank you.
  5. nomadreid

    I A gravity conundrum involving a solid cylinder

    Given a cylinder of height 2k with constant density and total mass M, and another object (for simplicity, a point mass) with mass m on the top of the cylinder; the force of gravitation is calculated between the centers of mass, which for the cylinder is at a distance k from the point mass...
  6. S

    Inverse square law of gravitation and force between two spheres

    I recently encountered this problem on a test where the solution for the above problem was given as follows: $$F= \frac{Gm_1m_2} {r^2} $$ (1) but $$ m=\frac{4}{3}\pi R^3 $$ substituting in equation (1) $$F= \frac{{G(\frac{4}{3}\pi R^3\rho})^2 }{2R^2} $$ where r=radii of the two spheres m=mass...
  7. AN630078

    Intensity of Stars and the Inverse Square Law Problem

    1. speed of light = 3*10^8 ms^-1 length of an Earth year=365 days*24 hours*60minutes*60seconds=3.15*1 0^7 seconds distance=speed*time 1 light year= 3*10^8 *3.15*10^7=9.46*10^15m 4.2 light years = 4.2*9.46*10^15m=3.9732*10^16m ~ 3.97*10^16m (to 3sf) 2. Intensity=power/area Power=1.4MW=1,400,000...
  8. K

    I Are there upper and lower limits to the inverse square law?

    Quoting from Modern Cosmology by Andrew Liddle on pages 130 and 131: "Let me stress right away that the luminosity distance is not the actual distance to the object, because in the real Universe the inverse square law does not hold. It is broken because the geometry of the Universe need not be...
  9. K

    I Questions about the inverse square law

    In "An Introduction to Modern Cosmology" by Andrew Liddle, page 130, paragraph A2.3 Luminosity distance, explains why the inverse square law does not hold at very far distances. One reason given is the expanding universe. (Another was the geometry of the Universe.) Could there be also...
  10. F

    B Is the inverse square law exact near a spherical body?

    I'm forking this off another thread where I brought it up but it was getting OT. It is good enough for a first approximation but it is certainly not exact. Consider a test mass one radius from a spherical body. Work out the contributions form two points diametrically opposed on the surface...
  11. M

    I How does the inverse square law apply to a focused detector?

    I am interested in evaluating light intensity variation in a digital image. A colleague wants to apply an inverse square law correction to account for distance variation. I am trying to justify that in this case, the inverse square law does not apply. Treating each pixel as a detector, it has...
  12. Clay

    I How do telescopes allow us to see light sources millions of light years away?

    i have heard how our broadcasts will be seen by aliens far away or whatever. but i realize those signals are going to "attenuate" by d^-2 anyway... how come in astronomy we can see light sources millions of light years away? shouldn't those signals be far too weak to detect after such a long...
  13. M

    Inverse Square Law with Half Value Layers for X-Rays

    Hello all, I have posted on Physics Forums a few times in the past, but mostly for help with my old physics classes and not anything in the real world. Part of my work involves radiography, but it is generally done in a field environment where we just shut down large sections of land to safely...
  14. J

    Does the inverse square law hold indefinitely for gravity?

    If the inverse square law for gravity varies with distance or distribution of matter, might the need for “dark matter” be obviated?
  15. H

    Question about Inverse Square law and sound intensity

    Homework Statement For school, I have to make a task about sound intensity and the distance to the sound source. I have to prove that the relation between these two is known as the inverse square law _1/ I_2 = ( _2/_1 )². Does someone know how I can plot the inverse square law or prove that it...
  16. F

    Wireless, RF, inverse fourth power law vs inverse square law

    When, in wireless communications, does the inverse fourth power-law become relevant? My understanding is that is that what cause the average signal power to degrade to the forth power is cancellation from self reflections. So by my way of thinking, an LOS point to point system, like a...
  17. S

    Investigation about the inverse square law of light radiation

    Homework Statement *Main ideas in bold[/B] Investigation of the inverse square law of light radiated from a light bulb. (done method, diagram, results and graph) Independent variable = the distance from the LDR (cm) Dependent Variable = resistance (k/ohms) Brief method: using an LDR, bulb...
  18. P

    I Gauss' theorem and inverse square law

    So, I know that the gauss law states that the Flux of the electric field through a closed surface is Q/ε , but does the gauss theorem works also for non inverse square law Fields? I think not because in order to not have a Flux depending on distance but a constant one we need that r^2 of the...
  19. T

    How Does the Inverse Square Law Apply to Calculating Distances Between Charges?

    I am faced with the following question: Two point charges X and Y, exert a force F on each other when they are at a distance d apart (x and y are opposite charges). When the distance between them is 20mm, the force exerted on each other is 0.5F. What is the distance d? I know that, e.g...
  20. G

    Inverse Square Law, Temperature Change, and Heat Source Temp

    I've been trying to wrap my head around the relationship between temperature increase of an object at a distance and temperature of a heat source. From what I've found, the temperature increase of an object from thermal radiation is affected by the inverse square law...
  21. InverseSquareLaw

    B Who Created the Inverse Square Law Theory

    I Am Wanting to Find out who Created the inverse square law.
  22. L

    I Inverse Square Law and various space dimensions

    I am interested in the derivation of the inverse square law in various dimensions via Green's functions. I think the trick is to imagine a sphere and then to integrate over it. Does anyone know a book or notes where this is explained? I found this below from here, but could not really...
  23. DavidReishi

    I Inverse square law and ensembles of photons

    I'm trying to visualize the effect of the inverse square law, not on a direct source of light, but on scattered light carrying visual data, such as that responsible for our everyday sight of things as well as our images of Earth from satellites. It seems to me that it should be true that, while...
  24. O

    I Evidence for Inverse Square Law at Extremely Large Distance?

    This is just an oddball question that's been rattling around in my head. What evidence do we have that the Coulomb force of, say, a spherical charge distribution Q, is actually nonzero at very large distances? I can easily imagine that the inverse square law is very accurate out to some...
  25. J

    Inverse square law in gravitation

    Help! Has anybody made a case as to why the inverse square law should apply to gravitation, a case that is based on pure reasoning, instead of empirical evidence? I have been trying to find such arguments, but no luck so far. Janein
  26. B

    Linearising an Inverse Square Law Graph for Gamma Radiation

    1. Homework Statement A piece of work I am doing for college (UK college that is) has me investigating the inverse square law for gamma radiation. I have collected data and the graph comes out looking right. I want to create a linearised graph of the data to investigate the results further. If...
  27. E

    Blackbody Radiation and the Inverse Square Law

    I am currently confused with the concept of the blackbody radiation and the inverse square law. Planck's function for the radiation of a blackbody is in ##W sr^{-1} m^{-3} ##, is this somehow a form of intensity (because of the watts per square meter unit)? If it does, doesn't intensity...
  28. Ebenshap

    How inverse square law is derived from area of sphere

    I almost understand how the inverse square law is derived from the area of sphere equation, 4πr2, but I'm not quite clear on what happens to the 4π. I found one equation that seemed to say that the intensity is equal to the area of the sphere of the source point times the amount of whatever...
  29. S

    Is Biot-Savart inverse cube or inverse square law?

    I know we can represent it two different ways. First: \mathbf{B} = \frac{\mu_0}{4\pi}\int_C \frac{I d\mathbf{l} \times \mathbf{\hat r}}{|\mathbf{r}|^2} If we open up unit vector, then it becomes: \mathbf{B} = \frac{\mu_0}{4\pi} \int_C \frac{I d\mathbf{l} \times \mathbf{r}}{|\mathbf{r}|^3} I...
  30. R

    Figuring out changes in Intensity (Inverse Square Law)

    Homework Statement If I measure a sound intensity of 1.0 at distance R from its source, what intensity would I measure at distance 3R in a free, unbounded space? What is the difference in decibels? Homework Equations I know that the equation for this is 10 (log R2/R1) The Attempt at a...
  31. R

    Inverse Square Law HELP PLEASE

    Homework Statement If I measure a sound intensity of 1.0 at distance R from its source, what intensity would I measure at distance 3R in a free, unbounded space? What is the difference in decibels? & If I measure a sound pressure of 1.0 at distance R from its source, what pressure would I...
  32. V

    Exploring Science in Movies: Finding the Perfect Film for Your Classroom Project

    Hello, I am in search of some movie suggestions that incorporate different concepts such as sound waves, magnetic fields, doppler effect, transmission of light, inverse square law. The movie doesn't need to necessarily incorporate all of those concepts. I am working on a school project and need...
  33. B

    How to show the inverse square law from a data set

    Homework Statement Hi there! I have a data set of r (independent variable) and E (electric field strength) (dependent variable). The question asks for a non graphical method to show if there is an inverse square law relationship between the two data sets. -- My attempt: I picked the equation...
  34. A

    Oscillations and inverse square law

    Homework Statement A particle of mass m moves in 1 dimension along positive x direction.It is acted on by a constant force directed towards origin with magnitude B,and an inverse square law repulsive force with magnitude A/x^2.Find equilibrium position. Homework Equations B+A/x^2=m*a...
  35. N

    Indoor Flower Garden & Plant Growth: Inverse Square Law

    Hi all looking for a bit of advice me the misses and the kids are starting a indoor flower garden and some herbs for the kids now my problems have come down to the lighting I have found out the colour spectrums needed as well as the luminous intensity required for heathly plant growth but the...
  36. H

    Inverse square law explains Olbers' paradox?

    Hello, This is the thread I originally wanted to respond to, but it's closed: https://www.physicsforums.com/showthread.php?t=650126 I also found this on Wiki-talk page, which seems to be the same argument...
  37. adjacent

    Transformers and inverse square law

    Homework Statement This was in my test paper today: A transformer is cut into half so that one half contains the primary coil and the other half contains the secondary coil. They are moved 30cm apart. Explain why the transformer would not work The Attempt at a Solution My answer: The magnetic...
  38. E

    Inverse Square Law: Calculating Intensity at Different Distances

    Homework Statement Problem One: Two kilometres away from a point source of infrared waves, the intensity is 4 Mw−2. Calculate the intensity 1m away from the source. Problem two: Light from a candle has an intensity of 20.0 units when a meter is placed 3.0m away. What is the reading on the...
  39. G

    Inverse Square Law: Total Power at Earth per Unit Area

    Homework Statement The intensity (I) of sunlight (the received power per unit area) drops with distance (d) from the sun according to the inverse square law - i.e I2/I1 is proportional to (d1/d2)^2 What is the total power received at Earth (above the atmosphere) per unit of surface area...
  40. T

    Inverse Square Law: Magnifying Glass & Sunlight

    I found this forum on Google. This may not be the right section so excuse me if so. I have a rather simple question though. When you take a magnifying glass on a sunny day and position it just right over a piece of paper, the paper will start to burn. Is the inverse square law (distance) the...
  41. Drakkith

    Inverse Square Law: Explaining Reduced Data Rate w/ Distance

    Quoting from Wiki, bolded section mine: What exactly is going on here with the data rate? Is it just the strength of the signal that is falling off as distance increases? If so, how does that reduce the data rates that can be used? If not, what limits the data rates?
  42. C

    Inverse Square Law - Calculating the solid angle

    Hi Everyone, For an individual inquiry and formal lab report task at school I have chosen to conduct an experiment to find out whether hot shoe mounted flash units follow the inverse square law and how the flash zoom is affected by the inverse square law. My first question is that In order...
  43. shounakbhatta

    Kepler's planetary motion and inverse square law

    Hello, The inverse square law of Newton's gravitational force, is it somehow related to each other? I mean to say P^2 is directly prop.a^3. Is it from the third law that the derivation of inverse sq.law of G=M.m/R2 is derived? Thanks.
  44. J

    How does distance affect light intensity according to the inverse square law?

    Homework Statement I have a general question about light and Lumens and the inverse square law? So Intensity = Initial Lumens/Lenth^2 So @ a Length of 1, there is no loss of light intensity. What unit is this 1. 1 meter? 1 foot? Homework Equations The Attempt at a...
  45. T

    Inverse square law resolves Olbers' paradox

    Treatment originally used to discard inverse square law as solution to Olbers' paradox was not set up correctly. If we include sensor (camera) in the treatment and model light as photons the result describes what we actually see.
  46. T

    Light in vacuum and inverse square law

    Does inverse square law apply to light in vacuum?
  47. L

    Incorporating Inverse Square Law In Gravity

    First of all, I'm 13 so I might not comprehend the complex vocabulary or symbols others might use. Second, I just joined! Okay, let's get to it. I think I know what the inverse square law is: if a number goes up by x, then the other number is the square of x but in the negative side...
  48. S

    Inverse Square Law: 1mW laser range?

    Hello PF! I've got a strange question for you physics boffins; assuming for a moment that lasers obeyed the inverse square law, what range would a typical 1mW red laser have in the atmosphere?
  49. M

    The inverse square law for point light sources inside an opaque medium

    Hello all, I already know that the radiant intensity of a point light source falls off with the inverse square of the distance to the source. This, however, only happens in a vacuum. My question is, what is the more general law for a point source inside an opaque medium with a known...
  50. B

    What is the relationship between force and distance in an inverse square law?

    I am confused regarding the following question. My guess is that b is correct, because the gravitational force equation has r^2. However beyond that I am not sure if any other options are correct. Please help What do you know about a force that follows the inverse square law. (a) The force...