NORTHERN ILLINOIS UNIVERSITY PHYSICS DEPARTMENT. Physics 211 E&M and Quantum Physics Spring Lab #2: Electrostatics. qq k r

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1 NORTHRN ILLINOIS UNIVRSITY PHYSICS DPARTMNT Physics 11 &M and Quantum Physics Spring 018 Lab #: lectrostatics Lab Writeup Due: Mon/Wed/Thu/Fri, Jan. 9/31/Jan. 1/, 018 Background You ve learned a lot about contact and field forces and we all experience the gravitational field force. However, electrostatic forces are not something we normally see primarily due to the fact that all objects are usually electrically neutral (equal number of positive and negative charges). One exception is static electricity, which all of us have observed in cold/ dry weather. This lab will explore some practical examples of electric forces and how to measure them, first discovered by Charles Coulomb in the late 1700 s! 1. Overview The electrical interaction between two charged particles is described in terms of the forces exerted between them. In 1783, Augustin Coulomb conducted the first quantitative measurements of these forces. He used a very sensitive torsion balance to measure the forces between two point charges, that is charged bodies whose dimensions are small compared to the distance between them. Coulomb found that the electrical force between two point charges is: Directly proportional to the product of the charges, inversely proportional to the square of the distance between them and always acts along a line joining the two charges. Mathematically we can express the magnitude of this force as, F qq k r 1 (1) where k is the coulomb constant and has a value of Nm /C, q 1 and q are the charges of point charge 1 and respectively, and r is the distance between the two charges. In order to understand Coulomb s Law, we need to note a few additional properties of the electrical charge. 1. There are two types of charge we call them positive and negative. Like charges repeal, unlike charges attract. 9

2 . Charge is quantized, that is we cannot isolate any smaller amount of charge than the charge of a proton (positive) or electron (equal in magnitude to the charge on a proton, but negative). 3. Charge is conserved. We can physically move it around, but we cannot create nor destroy it. 4. All matter is made of charged particles. Typically the positive and negative charges are present in equal numbers. When we say something is charged we mean it possesses a slight imbalance in the number of positive and negative charges. This lab experiment will simulate Charles Coulomb s experiment, using a less sophisticated version of his original equipment. Nevertheless, you will be able to determine the magnitude of the electrostatic force that Coulomb discovered. Graphite coated spheres will be electrically polarized by induction to produce an electrostatic force between them. The process used is similar in concept to the following: Figure 1: Charging by induction. Note how the sphere becomes polarized when the charged rod comes close. Notice how the excess charge forced to the opposite side of the sphere leaves the sphere when the wire is connected (the sphere is then grounded). In this lab, your "finger" will substitute for the "wire".

3 . Procedure Apparatus includes:. lectrostatics force chamber. Wooden guide block with graphite coated sphere attached. Suspended graphite coated sphere (pith ball). Rubber rod. wool, leather, cotton, and vinyl strips. Ruler. Magic wand (not show above) Typically the apparatus will be already set-up for you. Please be very careful the set-up is delicate. Some features of the set-up are: 1. A wooden guide block attached to a graphite coated pith ball.. A hanging graphite coated pith ball attached to a string in the center of the unit. 3. A mirror and scale attached to the back of the unit to eliminate measurement errors due to parallax. 4. Top cover to eliminate air currents. If the equipment is not already setup when you arrive, you will need to complete this step. 3

4 A. Polarization of a Sphere by Induction Write this section heading in your lab notebook:. A. Polarization of a Sphere by Induction. Write all questions asked below (underlined in blue) in your lab notebook under the proper section heading. 1. Stand the guide block with the attached sphere upright on the table. Then inductively charge the sphere attached to the guide block. Do this by rubbing the white vinyl strip with the wool square. Bring the sphere on the guide block near to the charged vinyl strip. DO NOT touch the strip to the sphere. When the sphere is close to the vinyl strip, simply touch the sphere with your finger. (You are acting as a ground here, see the inductive charging of one sphere in, Fig. 1. A ground can be thought of as an infinite sink into which to send charge that will never become filled.) Remove your finger from the sphere. After you have removed your finger from the sphere slowly pull the sphere away from the charged vinyl strip. The sphere on the guide block is now inductively charged. Work carefully if you touch the sphere to anything now it will immediately discharge and you will have to charge it again. Also work quickly, but not sloppily, as humidity in the air will allow charge to leak off of the spheres. Note: if, while the vinyl strip is close to the sphere, you hear a crackling sound, that means that the strip was close enough to the sphere for charge to jump the gap. That is, charge actually moved through the air from the strip to the sphere. The sphere is now uncharged and you will need to recharge the vinyl strip and repeat the process. This electrical discharge is very similar to what happens in an electrical storm. 3. Insert the charged sphere/guide block into the chamber. Note what happens just before the spheres touch. Do they attract or repel or do nothing? You will notice that just before the spheres touch, the uncharged (suspended) sphere will be drawn toward the charged sphere. This only happens at very short distances. These distances are considered short in comparison to the diameters of the spheres. xplain this attraction between the two spheres at a small distance? Do this by drawing the two spheres and show their charge distribution like in Fig Gently slide the charged sphere up to the suspended sphere and bring them into contact. When they touch, the same charge is equally distributed between the two spheres. ach sphere has the same amount of charge. Read through the Further xplanation section below before proceeding. 4

5 Further xplanation: The suspended sphere is initially uncharged. This does not mean that the sphere has no charged particles on it: it only means that the number of positively charged particles is the same as the number of negatively charged particles so the net charge is zero. When the charged sphere is brought near to the uncharged sphere the uncharged sphere becomes polarized. The like charges feel a repulsive force and are forced to the far side of the uncharged sphere, while the unlike charges are attracted to the near side of the uncharged sphere. Recall the sphere is a conductor. That means there are charges free to move about on the sphere. For conductors it is the electrons that are free to move about (not all electrons are free to move, it depends on the atomic structure of the conducting material). When electrons move to one side of the sphere under the influence of the electric force, the side they move to will acquire a net negative charge, while the side they move away from acquires a net positive charge. The unlike charges are much closer to the charged sphere than the like charges. A glance at q. 1 shows that distance really counts ( F 1/ r ) so the attractive force between the unlike charges is larger than the repelling force of the like charges. The spheres are attracted. Once the spheres have touched the charge carried by the sphere on the guide block is distributed equally between the two spheres and their like charges cause them to spring apart. Let us take a moment and think about why the charge is equally shared between the two spheres after they are brought into contact. Before they touch only one sphere was charged. The excess charges on that sphere felt repulsive forces between each other. Recall the sphere is a conductor and charge is free to move about. The excess charge moved until the net force on each was zero. This means that the excess charge on the sphere becomes equally distributed over the surface of the sphere. When the two spheres are brought into contact they become, momentarily, one large conducting surface. Now the excess charges have a larger area over which to distribute themselves. They will again move until the net force on each is equal to zero. Since the two spheres are equal in size this means distributing themselves equally over the surface of both spheres, which means each sphere gets an equal portion of the excess charge. Figure 3: Use the scale and mirror along the back wall to measure d and r. Note the difference between the distance d (distance the hanging sphere is displaced from equilibrium) and the distance r (distance between the centers of the two spheres) 5

6 Figure 4: Use the scale to measure d and r. Use the mirror along the back wall to help reduce parallax. 5. You have now successfully charged the hanging sphere. Using the Triboelectric Series from the Pre-Lab, deduce the charge (positive or negative) on the hanging sphere. Write your explanation in your lab notebook. 6. The Magic Wand is a mystery. It is not in the triboelectric series because we do not know what is inside it. You can induce a charge on the guide block sphere the same way you did with the vinyl strip (just turn it on and place it close to the sphere without touching it, then touch the sphere with your finger). Is the Magic Wand negatively or positively charged? C. Coulomb Force Measurement 1. In your lab notebook write the heading: ". C. Coulomb Force Measurement". For this section, make the following table in your lab notebook and also in an xcel spreadsheet: Position of Guide block ball XG (cm) Position of Hanging ball XH (cm) r (cm) d (cm) lectric Field F (N/C) Initial position of hanging ball = X0H = (put in your lab notebook and in xcel) 6

7 With the guide block removed from the chamber, record the position of the center of the hanging sphere as it freely hangs (Note: always measure to the center of the sphere!). When you take this measurement (and all future measurements), be sure that the image that you see in the mirror is directly behind the sphere itself this ensures that you are not taking your measurements at an angle. Call this variable X0H and record it in your lab notebook as well as on the xcel spreadsheet. You ll also need the length L of the pendulum. Use the ruler to measure straight down along the side of the box from the top to the center of the hanging sphere. Record this value in your lab notebook and in your xcel spreadsheet.. Charge the guide block sphere using either the vinyl strip or the magic wand. Then transfer the charge to the hanging sphere by letting the two spheres touch. It may be necessary to charge the two spheres several times to get a sufficient repulsive force. This is the case if bringing the guide block sphere into close proximity to the hanging sphere does not result in a reasonably large separation between the two. To increase the charge on the two spheres, keep charging the guide block sphere by induction then bring it into contact with the suspended sphere. If you cannot bring the two spheres into contact easily, they are already sufficiently charged. Note well, that if the repulsive force between the two spheres results in one of them hitting the side of the apparatus (or even the string of the hanging sphere hitting the apparatus) you have lost the charge on that sphere and you must start the charging processes over. The more charge on the suspended sphere the better. The greater the charge, the greater the displacement between the two spheres. This will result in better the resolution of your measurements. However, remember if the charge on the spheres, and thus the repulsive force between them, is sufficient you may cause the hanging sphere bounce around and hit the apparatus. It may take a bit of practice to get the right amount of charge on the spheres. A good rule of thumb is that if the separation between the two spheres is about cm then you have sufficient charge built-up on the spheres. The number of iterations required to build-up sufficient charge will depend greatly on the amount of moisture in the air. During a dry winter day one or two iterations will likely be sufficient. However, during a humid summer day five to ten iterations may be required. 3. Once you have charged the spheres sufficiently, then for several different values (at least 4) of the separation distance r, measure the displacement of the suspended sphere from equilibrium, d (see Fig. 3 and Fig. 4). Use your measurement of d to determine the repulsive electrostatic force, F (see q. 1 and the accompanying explanation below). Tabulate your results in the table in Part (1). 7

8 D. Analysis Figure 6: Forces acting on the hanging sphere. The distances d and r are also shown. We wish to analyze the dependence of the electrical force between the two spheres on the distance between the spheres. In order to do this we need a method to directly measure the force between the two spheres. Figure 6 shows a force diagram for the two spheres. We apply Newton s law s to develop the relationship (formula) giving the electrostatic force between the two spheres as a function of the suspended sphere s displacement from its equilibrium position, d. This allows us to determine the force, F, by direct measurement of the distance d. Looking at the Force diagram (Fig. 6) and applying Newton s nd law in component form we can see that (ignoring the small change in elevation of the hanging sphere): Fy T cos mg may 0 Fx F T sin max 0 () Where F is the electrostatic repulsive force between the spheres, and mg is the weight of the hanging sphere. Combining these equations results in: 8

9 F mg tan (3) We also note from the figure that d tan (4) L where d is the displacement of the hanging sphere from its equilibrium position, and L is the length of the hanging sphere's string. Combining qs. 3 and 4 gives F d mg L Assume that the mass of the hanging sphere is 15 mg (it was measured in the lab for your, and we will ignore the mass of the string). Write this value of mass in your lab notebook and xcel spreadsheet. 3. Questions 1. Plot a graph of the Coulomb force, F, as a function of the separation of the two spheres, r. That is, plot F vs. r. Comment on the graph. Does it look as you would expect? Why or why not.. Note that the Coulomb force law can be written as qq 1 1 F k ( kq ) ( kq ) r r r q q q. Can you fit your curve in xcel with a polynomial of order since 1? Note that xcel does not have that capability (it only allows positive orders). If we could have fit the curve, we could have extracted the net charge on the spheres from the coefficient in the fit. We will have to try another way. Go to the next problem. 3. Plot F vs. 1 r. Then you essentially are plotting the relation 1 F ( kq ) y m x b r where y F, m kq, x 1/ r, and b 0. Determine the charge on each sphere. Is the value reasonable? 9