Electrostatics Name Section Theory The study of charges at rest is called electrostatics. You are no doubt aware that objects can acquire excess amounts of charge by contact. What happens when you walk across a carpeted floor in the winter and then touch a metallic object? Ever stick a balloon to the wall after rubbing it in your hair? What about that annoying static cling? All of these situations involve the transfer of charge between objects (if charges move they are obviously not static anymore, but here we are only interested in what happens after the transfer - when they are again at rest). All matter is comprised of both positive and negative charges; atoms are basically a positively charged inner nucleus (protons carry the charge here) surrounded by negatively charged electrons. In most cases, atoms contain equal numbers of both so that as a whole they are electrically neutral. Charge gets transferred between objects in close proximity when they move relative to one another because one of the objects has a greater affinity for electrons than the other. For example, when a piece of rubber is rubbed with fur, some of the valence electrons in the atoms of the fur move to the rubber, leaving it with a net negative charge. The fur would have a net positive charge since some of its atoms now have a deficiency of electrons. Charge is always conserved, so that the total amount of charge on both objects would be the same (just different signs). It might surprise you that charge is quantized. No matter how much charge an object possesses, this total is made up of multiples of the fundamental charge 1.60 x 10 19 C. This is the amount of charge on a single proton or electron (the coulomb C is the SI unit of charge). Even though the masses of the proton and electron are vastly different, they both carry the same amount of charge. In this experiment, you will charge a conductor two different ways - by conduction and induction. Michael Faraday used a metal ice pail as a conductor in his investigations; a modern version is shown in Figure 1. It consists of two separate concentric wire mesh cylinders. The inner cylinder (on an insulated stand) represents the pail. The outer cylinder serves not only as a shield against extraneous charges or fields, but has a potential reference of zero (since it will be attached to ground). The zero potential reference is necessary since the charge sensor we will use does not actually measure charge, but potential (voltage); specifically, the potential difference between the red and black leads of the sensor. However, the measured voltage is proportional to the charge, and the sensor is sufficiently sensitive, capable of measurements in the range ±0.005µC at its highest gain. Lets see what happens when a negatively charged object is used with the pail. If this object is lowered into the pail without touching it, the negative charges (electrons) in the pail will move as far away as possible from the object - to the outer surface of the pail. This will leave a net positive charge on the inner surface of 1
Figure 1: The Faraday Ice Pail the pail. If we were then to provide a path away from the pail for the electrons (e.g., by touching the pail), the electrons would flow through us to ground. If we then removed our hand from the pail, then removed the object from inside the pail, the pail would be left with a net positive charge. This is charging by induction. This excess charge induced on the pail would reside on the outer surface of the pail - which is true of any conductor. Conversely, if we lower the object into the pail and let them touch, then electrons will flow from the object to the pail in an attempt to neutralize the object. When the object is removed, the pail would be left with a net negative charge (again, on the outside of the pail). This charging by contact is known as conduction. Apparatus Computer, Pasco 750 interface, Charge sensor, Stand, Data Studio software, Charge producers, Faraday ice pail, Ground wire. Procedure The charged objects will be the charge producers - these are the blue and white disks on the plastic (nonconducting) handles. After the disks are rubbed together, one will have a net positive charge, while the other will have a net negative charge (in roughly equal amounts). However, care must be exercised in their use: Rub the charge producers together briskly - but gently. Touch neither the disks themselves, nor the areas at which the disks connect to their plastic handles! In other words, use them as designed - by using the handles provided. The red lead of the charge sensor is connected to the pail; the black lead to the outer shield. The sensor has three GAIN settings - 1X, 5X, and 20X - selectable via a switch on the side. Make sure it is set to 1X. Clicking the Start button in Data Studio will begin data collection. The charge measured by the sensor (that on the outside of the pail) will be displayed graphically as shown in Figure 2. You can determine the amount of charge from the graph. 2
Figure 2: Charge Sensor Data The line in Figure 2 appears almost horizontal, but that is because the scale is too large. There are tools for rescaling the graph just below the Start button; there is also a Smart Tool that shows the graphical coordinates of the movable cross-hairs (to assist you in determining the magnitude of the charge). Figure 3 shows the graph rescaled and with the Smart Tool enabled. Figure 3: The Measured Charge (lowest point) is 0.0025µC Polarity 1. Ground the pail (with the yellow ground wire), which should zero the sensor. 2. Rub the charge producers together and then lower the white one into the pail (no contact) and leave it there. 3. Record the sign and magnitude of the charge as measured below (dont forget units!). 3
4. Repeat with the blue charge producer. White Blue 5. What happens when each charge producer is removed from the pail (as indicated by the sensor)? Charging by Conduction 1. Ground the pail. Rub the charge producers together. 2. Lower the white one into the pail. 3. Rub the producer against the inner surface of the pail. 4. What happens after you remove the producer? 5. Is it possible to increase the magnitude of the charge deposited by more rubbing of the producers or by moving the producer over the pail more? Why do you think this is so? 6. Record the sign and magnitude of the charge placed on the pail below. 7. Repeat the procedure with the blue charge producer. Record the sign and magnitude of the charge placed on the pail below. 8. How do the two charges placed on the pail compare? 4
Charging by Induction 1. Ground the pail. Rub the charge producers together. 2. Lower the white one into the pail (no contact) and leave it there. 3. What is the charge that the sensor measures? 4. With the producer still in the pail, ground the pail with a finger. Remove your finger, then remove the producer. What is the charge that the sensor measures? 5. How does this charge compare with the charge as measured before the grounding action? 6. Repeat the procedure with the blue charge producer. Record the charge induced on the pail below. Problem Two pith balls of mass m and charge Q are suspended by threads of length L and are separated by total angle 2θ. 5
1. Draw a free-body diagram for each pith ball. 2. Using Coulombs Law for the electrical force of repulsion and the weight of each of the pith balls, show that the charge on each sphere is mg tan θ Q = ±2L sin θ. k 6
Pre-Lab: Electrostatics Name Section 1. How many types of charge are there? 2. How do we differentiate between them? 3. What is the SI unit of charge? 4. Why are you more likely to notice electrostatic effects in the winter? 5. How many electrons are there in 1C? 6. What is a free-body diagram? 7