Charge! (The electric kind)

Transcription

1 Charge! (The electric kind) 1. Early Days of Electrical Phenomena. Modern Overview 3. Triboelectricity 4. Coulomb's Law 1. Early Days of Electrical Phenomena Phenomena associated with charged objects has been observed for millennia. The Greeks noticed that rubbing certain things together led to strange attractions. Fig. 1 It wasn t until the 18th century that science was able to deal with these phenomena analytically, predictively, and, of course, scientifically. Experiments Results from the experiments 1. Charge comes in two types: positive and negative. Positive charges repel other positive charges, and attract negative charges. 3. Negative charges repel other negative charges, and attract positive charges. 4. The attraction and repulsion depends on the distance between the two objects.. Modern Overview We can classify most materials into categories: Conductors Charges move very easily through a conductor. Metals are usually very good conductors. Also, ionic liquids conduct charge well. Insulators Charges do not move very much in an insulator. Glasses, ceramics, woods, rubber, & most plastics are examples of insulators. Pure water (deionized) is a good insulator too. Other types Semi-conductors Charges in semi-conductors can move around, but not as easily as in conductors. And, we can change how easily they move around. Silicon, Germanium are typical semi-conductors. Super-conductors updated on J. Hedberg 18 Page 1

2 negative ion positive ion In a super conductor, charge moves perfectly well (zero-resistance). However, it's hard to create these materials. The ones we do have only become superconducting at very low temperatures, so we can't use them for daily applications, yet. What's in an atom? The electrons and protons are the basic charges Electrons and protons are sub-atomic particles. The protons (along with neutrons) make up the positively charged nucleus of an atom. Fig. The electrons are distributed in space around the electron cloud. Ions When the number of electrons is equal to the number of protons, then an atom has no net charge. It is electrically neutral. If however, this ratio of positive and negative charges is not = 1, then the atom is an ion. This can happen if an electron from the electron is lost or added. Net charge Fig. 3 neutral negative positive Fig. 4 We can talk about the net charge of macroscopic object. If the number of positively charged species is the same as the negatively charged ones, then the object is charge neutral, and has no net charge. If however, there are more negative charges present in an object than positive charges, it will updated on J. Hedberg 18 Page

3 be macroscopically negative. The opposite situation will create a positively charged object. Atomic view of a conductor In a conductor, some electrons are allowed to move around. These free electrons are not bound to one particular nucleus, but instead can go visit different atoms. All metals are conductors. Other materials can be made conductive through special design. Fig. 5 Atomic view of an insulator In an insulator, the valence electrons of each atom are not allowed to wander throughout the material. Each electron is tightly bound to an atom. Insulating materials are very common. For the most part, plastics and glass and ceramic materials are all good insulators. Fig Triboelectricity updated on J. Hedberg 18 Page 3

4 Most of the situations in which we generate static electricity are due to the triboelectric effect. (tribo in greek means to rub). Bringing two materials in contact results in molecular bonding. If we break the bonds abruptly, it might lead to charge imbalance. Fig. 7 Material +Positive Affinity+ Polyurethane foam Hair, oily skin Nylon, dry skin Glass (soda) Fur Silk Paper (uncoated copy) Cotton Wool () Rubber Plastic Wrap Vinyl: flexible (clear tubing) Office tape backing PVC (rigid vinyl) Teflon -Negative Affinity- Triboelectricity Exactly how these bonds form and break depends on the materials. This lead to the creation of a triboelectric series table. Based on the position of the two materials on the table, we can say what the effects will be after we join, then separate the two materials. For example, if we were take something, nylon for example, from the upper part of the series, and touch it to something from the lower part, rubber, then the nylon will become positively charged and the rubber negatively. This table is obtained experimentally. The exact causes for this effect are still under investigation. Quick Question 1 If I wanted to put the most negative charges on my skin (which happens to be dry today), I should rub myself with: 1. Polyurethane foam. Nylon 3. Fur 4. Wool 5. Plasic Wrap Early tools - the electroscope updated on J. Hedberg 18 Page 4

5 Coulombic force A schematic view shows the path that charges can take to get to the gold leaf. conductors gold leaf Fig. 9 Fig. 8 The Electroscope. These three frames show the action of the electroscope in the presence of a charged objects. As the object is brought closer to the upper surface of the detector plate, its charges attract opposite charged from inside the conductor of the electroscope. This leaves the rest of the conductor imbalanced. Thus the two gold leaves at the bottom both become negatively charged. This action is known as polarizing (or induced charge). Fig. 1 Quick Question If I bring a wand close the collector plate of the electroscope, and the leaves move apart, what can I determine from this? 1. There is a positive charge on the wand. There is a negative charge on the wand 3. There is either positive or negative charge on the wand, but I can't tell which Induced polarization in insulators updated on J. Hedberg 18 Page 5

6 A similar effect can also occur in insulators. In an insulator, individual charges cannot move around so easily. However, the charges within each atom can. Fig. 11 If we bring a charged object near this oversized atom, we can imagine that the positive center might be brought a little bit closer, which the negative cloud of electrons is pushed away. Thus, the atom become polarized. Polarized Insulator charged object neutral insulator While the effect of each polarized atom on its own is tiny, if a large portion of the atoms in the insulator become polarized, then the effect will become larger. The insulator itself can be said to be polarized. positive side negative side Coulomb attempted to capture most of the phenomena of charges attracting and repulsing each other in a single equation. A torsion balance was used to detect the very small forces. Coulomb's Balance [1785] The torsion balance rotates due to a force applied at a distance (i.e. torque). There is a restoring torque due to the ribbon or fiber that the masses are suspended from. τ = κθ updated on J. Hedberg 18 Page 6

7 Quick Question 3 Two charged spheres (+Q on each) are brought near each other as shown. One is fixed on the balance arm which can rotate. In which direction is the torque acting on the balance? 1.. -x 3. +y 4. -y 5. +z 6. -z 4. Coulomb's Law If two charged particles have charges: q 1 and q, and are separated by a distance r, then the particles will each exert a force on each other with magnitude given by: k q 1 q F on 1 = F 1 on = where k is a constant and is given by: k = N m / C r Sometimes it will be written: 1 q 1 q F E = 4πϵ Here, the is the permittivity constant and it's equal to F/m ϵ r updated on J. Hedberg 18 Page 7

8 Quick Question 4 Which of the following is a plot of this function: y(x) = 1 x A +y C +y B +y D +y This is an inverse square law. Meaning: the force is proportional to the inverse square of the distance. F Direction (force is a vector) r Coulomb's Law, vector form What about the direction of the force? It is a vector after all right? The force between two charges will always be along a line connecting the two, but... We saw experimentally that sometimes the force was attractive, while other times it was repulsive. We found that if the object had the same polarity of charge, either pos or neg, then they repelled each other. If they had opposite charges, then they attracted. In vector form, Coulomb's law also gives the exact direction of the force, depending on the updated on J. Hedberg 18 Page 8

9 position of the two particle in quesiton. Radial Unit Vector 1 q F E = k 1 q r r If we want to define a vector with magnitude 1, that describes the position of particle 1 relative to particle, (basically a line going from point to point 1) we can do the following: r = r 1 r r 1 r This is the direction we need when referencing the force of charge on charge 1. Newton's Law of Gravitation was similar +y We've seen a similar situation in the context of the gravitational force between two massive bodies: F G force of earth on moon = Gm 1 m r r^earth to moon updated on J. Hedberg 18 Page 9

10 Quick Question 5 Which plot shows the gravitational force from the earth along the x axis? A x = C B D Directional nature of the force vector 1 1 Place two charges in space. Coulomb's Law dictates the force (mag and dir) between them. q F on 1 = k 1 q r^ r If, for example, q <, then the direction of the radial unit vector will flip, which shows the attractive nature of unlike charges. updated on J. Hedberg 18 Page 1

11 Quick Question 6 Which of the plots shows the force on a positive charge as a function of position along the x axis, given a positive source charge located at x =? A x = C B D Quick Question 7 +y Which of the following describes a unit vector pointing in the direction of the electrostatic force acting on charge 1. r = i + 4j r = 4 i + j r = + i^ r^ = + i^ 5 5 j^ j^ 4 6 updated on J. Hedberg 18 Page 11

12 Quick Question 8 +y Which of the following describes a unit vector pointing in the direction of the electrostatic force acting on charge 1. r =.5 i +.5j 4 r = i 3 j i 4 j 5 5 r = + r = 4i 3j 4 6 Here we have 3 charges: q 1, q, and q 3. Let s find the net electrostatic force on. If q 1, q, and q 3 are all positive, then there will be no net force on q 3. However, if q is negative, then the two force vectors will be pointed in the same direction. They will add together and create a net force towards q in the direction. q 3 updated on J. Hedberg 18 Page 1

13 Quick Question 9 Now we have two positive source charges located at +1 and -1 on the x axis. What is the electrostatic force on a positive charge as a function of position along the x axis? A x = -1 x = +1 C B D We can easily imagine using our vector tools to find the Net force due to many charges, all acting on each other. Quick Question 1 +y What direction would the net force F on a negative charge be if that charge were located at the origin (The two charges shown are equal in magnitude)? 1. Up and to the right.. Up and to the left. 3. Down and to the left. 4. Down and to the right. updated on J. Hedberg 18 Page 13

14 Quick Question 11 Where among the points listed should you put another positive charge q if you want the negative charge in the center to accelerate towards point A? q A E B D C Example Problem #1: Find the net force on q 3 due to q 1 and q. All charges have a magnitude of: 1 nc 1 cm 1 cm Example Problem #: electrons are positioned on the horizontal axis, each a distance l away from a central line, on which another electron is present. Where along the y axis is the electrostatic force on the third electron the greatest and the smallest. (besides y = ) updated on J. Hedberg 18 Page 14

15 Quick Question 1 A test charge q is positioned 1 meter from a fixed charge Q. While at this location, the test charge q, experiences a force of F from the stationary charge Q. The test charge is then moved to a new location meters from Q. What force will the test charge q experience from the stationary charge Q at the new location? F 4 F 1 F F 4F Example Problem #3: A negative charge is located between some positive charges as shown. If we pick the right h, then the system could be balanced Find an expression that gives the height h, in terms of d, B, and A. +B +A -q h d d h +B Quantization of Charge Electrons Electrons can be considered a particle. updated on J. Hedberg 18 Page 15

16 They have a mass: m e = kg. They do not have a well-defined size, so let s treat them like point particles. They also have a charge: e = C Electrons can move around. The SI Unit of charge is aptly named the Coulomb and is equal to charges. electron Protons Protons: They have a mass: m p = kg They are about 1.65 fm in diameter. They also have a charge: Protons don t move much. Example Problem #4: +e = C A 3.-mm-diameter Aluminum sphere has a net charge of +15 nc. What fraction of its electrons were removed in order to charge it? Any time we have a q, it better be a whole number multiple of electron charges. Conservation of Charge During these experiments, all we are doing is moving charges around the room. We are in no way creating or destroying charge. There is a set amount of net charge in the universe, and we cannot do anything to change that. (But, is the total equal to zero?) q = ne, n = 1,, 3 To The honble. Cadwallader Colden Esqr at New York... I send you by him, a Glass Tube; and enclose you the first Part of my Electrical Journal, which, rough as it is, may afford you some Amusement when you have a Leisure Hour. You will find in it, my Manner of Rubbing the Tube; to which I need only add, That it should be kept perfectly clean, and never sully d by Handling, &c. By the Time you have read and return d this, I shall have a second Part ready to send you, containing a greater Number of Experiments, and more curious. It is now discovered and demonstrated, both here and in Europe, that the Electrical Fire is real Element, or Species of Matter, not created by the Friction, but collected only.in this Discovery, they were beforehand with us in England; but we had hit on it before we heard it from them. What relates to the wonderful Effect of Points, the Difference between Candle Light and Sun Light, and several other Things in these Papers, the Philosophers at home, are still, as far as we know, ignorant of. I am, Sir, updated on J. Hedberg 18 Page 16

17 with great Respect Your obliged and most humble Servant B Franklin [ updated on J. Hedberg 18 Page 17