Coulomb's Law -112

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Coulombs Law - the Impact Distance has on Force PHY 112 Ruben Osorio Professor Blakeney February 6, 2023 Osorio 1

Purpose We are aiming to further verify Coulomb’s Law which takes into account to separate objects with a charge and we observe the impact that distance between the charged objects has on the resulting force. We know that there are two charges: positive and negative - opposite charges attract and like charges repel. This is a very important piece of information for many f ields: physics, chemistry, and biology. This lab we will obtain data from a system displaying static-electric force, and we will graph the data in order to experimentally test Coulomb’s Law. Materials - Balloon - Fishing line - Pith ball - Fine needle - Tape - Ruler - Hair, fur, or wool Procedures This lab requires the objects stated above, and in order to start make sure you have obtained the materials. First step a day or two before performing the experiment make sure to f latten out the f ishing line under some books until experiment day. You can also use an iron to f latten out the line the day of, but be careful of it melting. Then poke the f ine needle through the pith ball to create a canal for the f ishing line to thread through. Then you will be able to hang the line so that the pith ball is evenly distributed with the same amount of line on each side, but be cautious to tape the ends at the same angle. Once the pith ball is Osorio 2

hanging the forces acting on it will be gravitational and tensional forces. We will be provide another force using the balloon, so you will have to in f late the balloon. Now for the actual experiment - rub the balloon on your hair or fur or a piece of felt in order to give the balloon a net negative charge and tap the pith ball in order to give it a negative charge so that it will be repelled by the balloon. Then take out your ruler and either place it to monitor the changes that are about to occur or have a partner measure each time. Charge up the balloon by rubbing it on your desired material and bring the balloon closer to the pith ball and take six measurement of the distances between the ballon and the pith ball (r) and the change in distance of the pith ball from its original position (d). When recording these measurements be careful not to touch the ballon to the ball otherwise you will have to rerecord all the data. Don’t forget the units that must be used, meters not centimeters, so you must convert centimeters to meters. Then calculate the static force using the equation: Fstatic=mgd/L - d is the distance in meters between the two charged molecules. Then create a graph of the calculated static force on the y-axis and the distance between the charged objects on the x axis. The static force is the dependent variable and the distance between the charged molecules would be the independent variable because the force depends on the distance. The controls for this experiment are the mass of the pith ball and the hanging system. Then create one more graph of the static force again, but this time against the distance between the charged objects inverted and squared (1/r^2). Osorio 3

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Photographs of Experiment Data Static Force vs r Distance Between Charged Objects (m) Static Force (N) 0.065 2.96E-05 0.06 4.45E-05 0.05 5.63E-05 0.045 5.93E-05 0.04 6.52E-05 0.035 8.89E-05 Osorio 4

Static Force vs inverse r^2 Calculations The following calculations will be to determine the static force, and show how to calculate the inverse square of the distance between the charged objects. We know that the static force is equal to the gravitational force times tangent of the angle of the string at a speci f ic d. Fstatic=(mg)(tanØ) However we don’t know what the exact angle is, but we know tangent is opposite/adjacent of a triangle and the comes out to be d (displacement of pith ball from no static force acting on it to a static force acting on it) over L (vertical length from string to pith ball). Fstatic=(mg)(d/L) The mass of the pith ball is .15 grams which is .00015 kg and g is 9.8 N/kg, the value for d changed for every instance I recorded and L was measured at 49.6 cm which is .496 meters. The d value I will use for the calculation will be .02 meters which was when r was .045m giving us this problem Fstatic =.00015kg X 9.8N/kg X .02m /.496m Inverse Squared of Distance Between Charged Objects (1/m^2) Static Force (N) 236.7 2.96E-05 277.8 4.45E-05 400.0 5.63E-05 493.8 5.93E-05 625 6.52E-05 816.3 8.89E-05 Osorio 5

As you can see the kg and meters cancel out giving us the units of force which is Newtons, N. The quantity of static force resulting from that equation being 5.93x10^-5 N. Another calculation, more simple, is f inding the inverse square of r, the distance between the two charged molecules. I will use the r related to the d value we used in the last equation. The r value is .045m. 1/r^2 = 493.83 Graphs Osorio 6 0.00E+00 1.00E-05 2.00E-05 3.00E-05 4.00E-05 5.00E-05 6.00E-05 7.00E-05 8.00E-05 9.00E-05 1.00E-04 0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 Static Force (N) r (m) Fstatic vs r 0.00E+00 1.00E-05 2.00E-05 3.00E-05 4.00E-05 5.00E-05 6.00E-05 7.00E-05 8.00E-05 9.00E-05 1.00E-04 0 100 200 300 400 500 600 700 800 900 Static Force (N) 1/r^2 (1/m^2) Static Force vs inverse r^2

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Results In the f irst graph we did not acquire a linear graph when just putting the force against the distance between the two charged objects. In the second graph we acquired a linear correlation between the static force and the inverse square of the distance between the two charged objects. Conclusion This experiment touches base on charge interactions and how electrostatic force changes with the distance between the charged objects. There are two types of charges: positive and negative, and the way they interact is key information for many things. Opposite charges attract and like charges repel meaning a net positively charged object will be attracted to a net negatively charged object, however if there are two net positively charged or two net negatively charged objects they would repel each other. This explains why the pith ball and balloon were repelling each other as opposed to attracting each other. In this lab we make a balloon net negatively charged by rubbing it on our head or on fur or felt and how does this happen? Do the protons leave so that there are more negatively charged particles? Well it is actually a transfer of electrons, the negatively charged particles. This lab analyzes how the distance between the two charged objects correlates to the static force, and that is why the this lab is called Coulomb’s Law because that is exactly what Coulomb’s Law describes. The equation is Fe=kq1q2/(r^2) This equation shows that if we doubled the distance between the two charged objects that the force wouldn’t decrease by half, but due to r being to the power of two the force will decrease by four (which is two to the power of two). Our graphs were meant to show us whether or not coulombs law is true. If the static force directly linearly with the distance between the two charged objects then my f irst Osorio 7

graph would have been linear, but it was not. The second graph however, was linear. The y-axis was the static force and the x axis was the inverse square of the distance between the charged objects and the experimentally obtained data were pretty close to being fully linear meaning that the force depends on the inverse square of r. There de f initely was a linear trend, the furthest, closest, middle, and furthest data points were practically a perfect line with the other points being slightly o ff the line. This graph is experimental proof that forces is directly proportional to the inverse square of the distance between the two charged objects. This lab being done at home was cause for some errors such as the line not being perfectly straight, and not being one hundred percent sure that the angels matched on the f ishing line. It was also somewhat di ff icult for me to get the measurement. I taped a ruler to a trashcan which was around the same height as the pith ball so that I could measure the change in distance by a video recording that I took. I tried to keep my hadn’t as still as possible and tried to wait for the balloon to stop moving before moving it further towards the balloon, but in the video it was sort of di ff icult to see the exact measurement which could have lead to some larger or smaller measurements in comparison to the truth. Analysis Questions Response - If I were to repeat this experiment with the exact same r values it is likely that my force values won’t be the same. This is expected because I can’t ensure the charges of the balloon or pith ball will be the same as they were conducting it the f irst time. The equation for Coulomb’s law shows four variables a constant variable, the charge values for the two objects and the distance between the two objects. If we can have r be the same we would need the charges of the objects to also be the same if we wan the same static force. Osorio 8

1. If the distance between the balloon and the pith ball doubles, what will happen to the static-electric force? Explain your answer. - If the r value, distance between the balloon and pith ball, were to double we know that the static-electric force would decrease by four. We can think of this in two ways: qualitatively and quantitatively. Qualitatively: The force is strongest closest together so if we put the objects further away it will have a weaker force. So we know that the force would decrease but by how much, for that we have to use the equation. Quantitatively: Coulomb’s Law has an equation with a constant and then variables that change q1 and q2 are the charges of the objects and if one of those were to double then the force would double, but if the distance between the charges double the force would decrease by four. We know this since when r is squared and inverted it is proportional impacts the static force. Fe=kq1q2/(r^2) if r doubles then Fe decreases by a factor of 4. Osorio 9

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