# What is the mathematical relationship between distance and intensity

### Electric Field Intensity

So if separation distance increases by a factor of 2, the electric field strength of the inverse square relationship between electric field strength and distance to both the concept of an electric field and the mathematics of an electric field. The inverse-square law, in physics, is any physical law stating that a specified physical quantity or intensity is inversely proportional to the square of the distance It is also a fading of the distance and mathematical to the source. used with any physical quantity that acts in accordance with the inverse-square relationship. The intensity or brightness of light as a function of the distance from the light source See a mathematical derivation of the intensity and distance relationship.

The gravitational attraction force between two point masses is directly proportional to the product of their masses and inversely proportional to the square of their separation distance.

The force is always attractive and acts along the line joining them. If the distribution of matter in each body is spherically symmetric, then the objects can be treated as point masses without approximation, as shown in the shell theorem.

Otherwise, if we want to calculate the attraction between massive bodies, we need to add all the point-point attraction forces vectorially and the net attraction might not be exact inverse square.

## Inverse-square law

However, if the separation between the massive bodies is much larger compared to their sizes, then to a good approximation, it is reasonable to treat the masses as a point mass located at the object's center of mass while calculating the gravitational force. As the law of gravitation, this law was suggested in by Ismael Bullialdus.

Indeed, Bullialdus maintained the sun's force was attractive at aphelion and repulsive at perihelion. Hooke's Gresham lecture explained that gravitation applied to "all celestiall bodys" and added the principles that the gravitating power decreases with distance and that in the absence of any such power bodies move in straight lines.

We will set up two lights of known luminosities.

### The Inverse-Square Law

The null-photometer is placed between the lights, and moved to the point where both halves of the window are equally bright. The distances from the photometer to the lights are then measured.

Finally, the luminosities and distances are substituted into the equation just derived; if the law is correct, the two sides should be equal, or nearly equal if we allow for experimental error.

The null-photometer is placed between the two lights and moved until both halves of the window have the same brightness. Testing the law To test the law properly, we will set up several pairs of lights, with each pair separated from the others to avoid confusion.

**A Level Physics - Wave Amplitude and Intensity**

You will find this experiment easier if you work with a partner; one person can hold the photometer in position, while the other measures the distances to the lights. However, you and your partner should switch roles so that everyone gets a chance to do every measurement.

When you make measurement, hold the null-photometer between the lights, and move it back and forth along an imaginary line between them until both halves of the photometer's window appear the same.

## Relationship Between Sound Intensity and Power?

Your partner can check to make sure the photometer really is on a line between the two lights, and then measure the distances Da and Db. Ideally, these distances should be measured from the center of each light-bulb to the nearest side of the photometer, as shown in the diagram. Once both distances have been recorded, flip the photometer over so the left face is now the right face, and vice versa.

Re-position the photometer between the lights, move it so both halves appear the same, and again measure the distances. Repeat two more times, again flipping the photometer each time. You should now have four separate measurements of the two distances. Each set of four measurements can be averaged to get a more precise value; you can also look at the range of values for each measurement to get some idea of the accuracy of your work.

Before moving on to the next pair of lights, be sure to record the luminosities La and Lb. When you write up your lab report, first compute averages for your measurements of Da and Db for each pair of lights. If the last two columns of each row are equal, allowing for experimental error, then the inverse-square law passes the test. Measuring luminosity The same procedure can be used to measure the luminosity of a light-bulb.

We will set up a pair of lights and tell you the luminosity of one light; your job is to calculate the luminosity of the other.

Follow the same procedure you used when testing the law: Record your measurements for Da and Db, along with the known luminosity La. When you write up your lab report, compute averages for your measurements of Da and Db just as you did when testing the law. And like all formulas, these electric field strength formulas can also be used to guide our thinking about how an alteration of one variable might or might not affect another variable.

### What is the relationship between light intensity and distance from the light source?

One feature of this electric field strength formula is that it illustrates an inverse square relationship between electric field strength and distance. The strength of an electric field as created by source charge Q is inversely related to square of the distance from the source. This is known as an inverse square law. Electric field strength is location dependent, and its magnitude decreases as the distance from a location to the source increases.

And by whatever factor the distance is changed, the electric field strength will change inversely by the square of that factor. Use this principle of the inverse square relationship between electric field strength and distance to answer the first three questions in the Check Your Understanding section below.

The Stinky Field Analogy Revisited In the previous section of Lesson 4, a somewhat crude yet instructive analogy was presented - the stinky field analogy.

The analogy compares the concept of an electric field surrounding a source charge to the stinky field that surrounds an infant's stinky diaper. Just as every stinky diaper creates a stinky field, every electric charge creates an electric field. And if you want to know the strength of the stinky field, you simply use a stinky detector - a nose that as far as I have experienced always responds in a repulsive manner to the stinky source.

In the same way, if you want to know the strength of an electric field, you simply use a charge detector - a test charge that will respond in an attractive or repulsive manner to the source charge. And of course the strength of the field is proportional to the effect upon the detector. A more sensitive detector a better nose or a more charged test charge will sense the effect more intensely. Yet the field strength is defined as the effect or force per sensitivity of the detector; so the field strength of a stinky diaper or of an electric charge is not dependent upon the sensitivity of the detector.

If you measure the diaper's stinky field, it only makes sense that it would not be affected by how stinky you are. A person measuring the strength of a diaper's stinky field can create their own field, the strength of which is dependent upon how stinky they are.

But that person's field is not to be confused with the diaper's stinky field. The diaper's stinky field depends on how stinky the diaper is. In the same way, the strength of a source charge's electric field is dependent upon how charged up the source charge is. Furthermore, just as with the stinky field, our electric field equation shows that as you get closer and closer to the source of the field, the effect becomes greater and greater and the electric field strength increases.

The stinky field analogy proves useful in conveying both the concept of an electric field and the mathematics of an electric field. Conceptually, it illustrates how the source of a field can affect the surrounding space and exert influences upon sensitive detectors in that space.

And mathematically, it illustrates how the strength of the field is dependent upon the source and the distance from the source and independent of any characteristic having to do with the detector.

The Direction of the Electric Field Vector As mentioned earlier, electric field strength is a vector quantity. Unlike a scalar quantity, a vector quantity is not fully described unless there is a direction associated with it. The magnitude of the electric field vector is calculated as the force per charge on any given test charge located within the electric field. The force on the test charge could be directed either towards the source charge or directly away from it.

The precise direction of the force is dependent upon whether the test charge and the source charge have the same type of charge in which repulsion occurs or the opposite type of charge in which attraction occurs. To resolve the dilemma of whether the electric field vector is directed towards or away from the source charge, a convention has been established.

- Inverse Square Law Formula
- Electric Field Intensity
- The Inverse-Square Law

The worldwide convention that is used by scientists is to define the direction of the electric field vector as the direction that a positive test charge is pushed or pulled when in the presence of the electric field.