Electrostatics ~ Learning Guide Name: Instructions: Using a pencil, answer the following questions. The Pre-Reading is marked, based on effort, completeness, and neatness (not accuracy). The rest of the assignment is marked, based on effort, completeness, neatness, and accuracy. Every time you see a bold word, make sure you refer back to your "Submission Requirements." Do your best! Introduction to Charges 1. Describe the three main constituents of the atom. Discuss how each part can contribute to an objects overall charge. Of the three constituents, which part has the most active role in creating a charge? Discuss why you choose this way by stating how Newton s First and Second Laws impact this charge more so than the other two. 2. Outline the procedure used to charge two balloons in two ways; charge by conduction, charge by induction. Be sure to sketch enough diagrams to illustrate each step in the procedure. You only have the following equipment. Three balloons initially neutral Your hair Two large anti-static mats big enough for you and /or the balloons. By Conduction: By Induction Page 1 of 17
3. When an ebonite rod is rubbed with fur, the rod becomes negative and the fur becomes positive. Using an ebonite rod and fur describe what procedure you would need to follow to determine the sign of the charges on each balloon used above and your hair. Again, sketches of the set-up would be helpful 4. A charged object will attract a neutral object. a) We know that it is only electrons that move significantly in electrostatic interactions. Provide two reasons why the protons remain basically stationary. b) Coulomb s law, F = kq 1 Q 2 /R 2, describes how the force is related between two POINT charges. What kind of relationship exists between this force, F, and the separation between the charges, r? Draw a detailed diagram that shows exactly how a charged object attracts a neutral object by drawing a diagram showing how the charges arrange themselves, and by using Coulomb s Law to explain why an attraction occurs and not a repulsion. Use the simulation entitled Balloons and Static Electricity found in Lab Resources for this unit. Page 2 of 17
5. A (positively or negatively) charged rod is brought up to the same distance from each set of metal spheres as shown in separate situations below. The spheres in each pair are initially in contact, but they are then separated while the rod is still in place. Then the rod is removed. Rank the net charge on each sphere from most positive to most negative after the spheres have been separated and the charged rod removed. Positive 1 2 3 4 5 6 Negative Or, all spheres have the same charge. Please carefully explain your reasoning. Page 3 of 17
6. The following diagrams show three separate pairs of point charges. The pairs only interact with each other since they are far apart. Rank the force on each point charge from most attractive to most repulsive. Highest 1 2 3 4 5 6 Lowest Or, all of these charges experience the same force. Please carefully explain your reasoning. Page 4 of 17
7. Demonstrate with Coulomb s Law what happens to the magnitude of the force between two charges Q1and Q2 separated by a distance R if: (a) one of the charges is doubled? (b) both charges are doubled? (c) separation distance is doubled? (d) separation distance is tripled? (e) both charges are doubled and separation distance is doubled? (f) both charges are doubled and separation distance is halved? (ans: (a) 2F,(b) 4F, (c) F/ 4, (d) F/ 9, (e) F, (f) 16F ) 8. Two small spheres are located 0.50 m apart. Both have the same charge on them. If the repulsive force is 5.0 N, what charge is on the spheres, in µc? (ans: 12 µc) 9. Let s compare this electrical force to the force of gravity. Imagine you could place 1g of electrons 1.0 m away from another 1g of electrons. Calculate: (a) the electrical force of repulsion between the two charge collections; (ans: 2.9x10 26 N) (b) the gravitational force of attraction between them; and (ans: 6.7 x 10-17 N) (c) the ratio of the electrical force to the gravitational force. (ans: 4.3 x 10 42 : 1!!!) (d) Discuss whether you think gravity would play a major part in holding atoms together. Refer to your results above. Page 5 of 17
10. One electron has a mass of 9.1 x 10-31 kg. How many coulombs of charge would there be in 1 kg of electrons? How much force would this charge exert on another 1 kg of electrons 1.0 km away? (This is strictly an imaginary situation.) (ans: 1.8 x 10 11 C, 2.8 x 10 26 N) 11. Electric Force is a vector. Three charged objects are located at the 'corners' of an equilateral triangle with sides 1.0 m long. Two of the objects carry a charge of 5.0 µc each. The third object carries a charge of 5.0 µc. Assume all three objects are very small. a. Draw the three charges below. Draw the forces acting on the 5.0 µc charge. b. Using you diagram above draw the vector diagram showing how you would arrive at the direction of the Net Force acting on the 5.0 µc charge. Determine the angles inside your vector diagram and label them directly onto the sketch. c. What is the resultant force acting on the 5.0 µc object?(ans: 0.39 N directed along a line bisecting adjacent sides) Page 6 of 17
12. Two small spheres, each of mass m and positive charge q, hang from light threads of lengths l. Each thread makes an angle θ with the vertical as shown above. a. On the diagram draw and label all forces on sphere I. Label the distance, r, that you would use to determine the magnitude of the electric force acting between both spheres. b. Determine the mass, m, for the charges, q if q = 400µC, l = 2m, and θ = 30. (ans: m = 63.6kg) Page 7 of 17
Electric Fields 1. For point charges we have two equations so far; Coulomb s Law, F = kq 1 Q 2 /R 2, and the Electric Field, E = kq/r 2. Both equations represent vector quantities. Explain why we only need one charge, Q, to calculate the electric field, E, while two are required to calculate F. Examine the units for each vector to assist you with an explanation. Ultimately I want to know what the difference between E and F is conceptually. 2. E = kq/r 2 is the equation for the electric field surrounding point charges. a) What is the relationship between E and the distance away from the charge, R? Explain with an example. b) Electric field lines point away from positive charges and towards negative charges. Draw the E-field vectors at the locations labelled a, b, and c below. Use dotted lines to show the individual E-field vectors from each charge, then use a solid line to show the Net E-Field at each location. Page 8 of 17
c) Now sketch the field lines onto the above diagram. Include one line that passes through all three points. What is the relationship between the shape and direction of the field lines and Net Electric Field at each point in space? 3. Given below are seven arrangements of two electric charges. In each figure, a point labeled P is also identified. All of the charges are the same size, 20 C, but they can be either positive or negative. The charges and point P all lie on a straight line. The distances between adjacent items, either between two charges or between a charge and point P, are all 5 cm. There are no other charges in this region. There is no charge at point P, nor are there any charges in this region. Rank these arrangements from greatest to least on the basis of the strength of the strength of the electric field at point P. That is, put first the arrangement that will produce the strongest field at point P, and put last the arrangement that will produce the weakest field at point P. Strongest 1 2 3 4 5 6 7 8 Weakest Please carefully explain your reasoning. Page 9 of 17
4. An electron carries a charge of 1.6 x 10-19 C. If a force of 3.2 x 10-17 N causes the electron to move upward, what is the magnitude and direction of the electric field? (ans: 2.0 x 10 2 N/C, down) 5. Consider the diagram below to answer the questions that follow. a. Sketch the electric field vectors from each charge at location A. Be sure to sketch them roughly to scale. Show the direction of the Net Electric Field. Lightly sketch in the field lines onto the diagram above. b. Determine the angles of the vectors above and label them on the diagram above. c. What is the resultant electric field strength E at point A inthe figure below? Give both the magnitude and the direction.(ans: E A = 2.6 x 10 5 N/C, 11 o left of the vertical and upward) d. If an electron was place at location A what would be its acceleration? Give both magnitude and direction. (ans: 4.57 x 10 16 m/s 2 in a direction 180 degrees from the above direction) Page 10 of 17
e. Discuss the similarities and differences between this question and question 11 in the previous section. In particular, describe what you actually calculating when you calculate Electric Force as opposed to Electric Field. 6. Sketch two oppositely charged parallel plates. Draw in the electric field lines being sure to adhere to the rules regarding their direction and relative strength. Discuss how the field between the plates near the positive plate compares to the field near the negative plate. 7. For the above set of plates why can t we use the formula E=kQ/r 2 to determine the value of the electric field between the plates? What formula should we use? Electric Potential Energy 1. Unlike Electric Fields or Electric Forces, the Electric Potential Energy (measured in Joules) is a scalar quantity. However, it can still be positive or negative even though it does not have a specific direction. a. What is the formula to determine the Electric Potential Energy between two point charges? How does one determine the sign of this energy? b. Two non-zero charges are separated by a distance r. The electric potential energy is measured to be basically zero between these charges. What must be true about the arrangement of these charges? Page 11 of 17
2. Consider two oppositely charged parallel plates. This is often referred to as a parallel plate capacitor. a. Energy can be defined as the ability to do work. Do two charged plates contain energy? Give an example of how they can do work. b. In order to store more energy in a parallel plate capacitor whose plates differ by a fixed voltage, what change(s) would you make in the plates? 3. Equipotential lines are like contour lines on a map which trace lines of equal altitude. In this case the "altitude" is electric potential or voltage. Equipotential lines are always perpendicular to the electric field. In three dimensions, the lines form equipotential surfaces. Movement along an equipotential surface requires no work because such movement is always perpendicular to the electric field. a. Consider two opposite charges separated by a distance r. Find a point where the Electric Potential equals zero. Remember V = kq/r for point charges. This is a SCALAR quantity whose sign is determined by Q. b. Is the Electric Field zero at this point? Explain what would happen if a tiny positive charge was placed at this location. Page 12 of 17
c. The definition of Electric Potential, V, is given by the equation V = E p /Q. It is the Electric Potential Energy per Coulomb of charge. How can an object be at zero potential and yet still be experiencing a force (wanting to move)? Use the 3-D electric potential diagram for two opposite charges show below. The positive charge is the one at the back of the picture. It shows that the potential drops off like a steep mountain or hill. The negative charge shows a well. 4. How much work is needed to bring a + 5.0 µc point charge from infinity to a point 2.0 m away from a + 25 µc charge? (ans: 0.56 J) 5. How much potential energy would an electron in a hydrogen atom lose if it fell toward the nucleus from a distance of 7.5 x 10-11 m to a distance of 5.0 x 10-11 m? (ans: - 1.6 x 10-18 J or - 10 ev) Page 13 of 17
6. Consider an electron between the plates of a charged capacitor. The figures below show situations where the potential across the capacitor, and the separations between the capacitor plates, vary. Specific values are given in each figure. Rank according to the magnitude of the electric potential energy of the electron. Greatest 1 2 3 4 5 6 Least Or, all of the electric potential energies are the same. Please carefully explain your reasoning. Page 14 of 17
7. An electron-volt, ev, is a unit of measure. What quantity does the electron volt measure? What is the conversion between ev and the standard unit for this quantity? 8. What is the difference between Electric Potential, Electric Potential Difference, Voltage, and Electric Potential Energy? 9. A proton is travelling at a speed of 4 x 10 5 m/s moves into a series of charged parallel plates as shown below. a. What is the impact speed on the third plate? (ans: 6.7 x 10 5 m/s) b. The same proton is fired again at the same speed towards a very large nucleus (parallel plates removed) and comes to rest 0.15 nm away from the atom. What is the charge of the atom? (ans: 1.4 x 10-17 C or 140 x 10-19 C) c. What might this nucleus be? (use the periodic table) (ans: Ra) d. Why can you not use high-school kinematics to get the answer above for this situation? Page 15 of 17
Putting it all Together 1. In a television set, electrons are first accelerated from rest through a potential difference in an electron gun. They then pass through deflecting plates before striking the screen. a. Determine the potential difference through which the electrons must be accelerated in the electron gun in order to have a speed of 6.0 x 107 m/s when they enter the deflecting plates. (ans: 10200 V) The pair of horizontal plates shown below is used to deflect electrons up or down in the television set by placing a potential difference across them. The plates have length 0.04 m and separation 0.012 m, and the right edge of the plates is 0.50 m from the screen. A potential difference of 200 V is applied across the plates, and the electrons are deflected toward the top of the screen. Assume that the electrons enter horizontally midway between the plates with a speed of 6.0 x 107 m/s and that fringing effects at the edges of the plates and gravity are negligible. b. Which plate in the pair must be at the higher potential for the electrons to be deflected upward? Check the appropriate box below. Upper plate Lower plate Justify your answer. Page 16 of 17
c. Considering only an electron's motion as it moves through the space between the plates, compute the following. i. The time required for the electron to move through the plates. (ans: 6.67x10-10 s) ii. The vertical displacement of the electron while it is between the plates. (ans: 6.5x10-4 m) d. Show why it is a reasonable assumption to neglect gravity in part c. e. Still neglecting gravity, describe the path of the electrons from the time they leave the plates until they strike the screen. State a reason for your answer. f. What two adjustments could be made in the experiment to make the overall deflection smaller and in the opposite direction? Page 17 of 17