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Lesson 2: Coulomb’s Law Physics 30 Outcome 1 Lesson 2: Coulomb’s Law Hewitt-Drew-it! PHYSICS 88 Coulomb's Law Charge: Symbol unit Rule for using charge in the Physics 30 formulas: Charles-Augustin de Coulomb Born on June 14, 1736, in Angoulême, France, Charles-Augustin de Coulomb studied engineering and plied his trade with the military before winning accolades for his work in torsion balances. He offered pioneering theories in the force found between electrical charges, as well as magnetic attraction and repulsion. The unit of measurement known as the coulomb is named in his honor. He died in Paris on August 23, 1806. Part 1: Coulomb’s Torsion Balance: Explain how Coulomb’s Torsion Balance was used to determine the force between two charged spheres: Lesson 2: Coulomb’s Law Physics 30 Outcome 1 Part 2: The Coulomb Experiment Variables Activity: The Physics Classroom Coulomb’s Law Interactive Google “Coulomb's Law Interactive - The Physics Classroom” to access the Coulomb’s Law app. Draw the frame to be a larger size so your whole group can see it on the screen. The app starts out with a positive and negative charge. Manipulated QUESTION 1: What is the magnitude of each charge? Which charge is larger? Controlled Responding Move them closer together until you see force arrows. QUESTION 2: Which way do the force arrows point and how do their sizes compare to each other? Is this result expected? Is there a law of physics that explains/predicts this? Move the charges around, changing the distance between them so they are closer together and further apart. Gather data from at least 8 points and plot the force as a function of distance using the graph below. Note that separation distance is the distance between the centres of the objects. Distance (m) Force (N) Use your graphing calculator or Desmos to plot each of the following graphs. Sketch the results below Linear Quadratic Inverse Square QUESTION 3: Which of the three graph types above looks the most like your graph of force as a function of distance? Lesson 2: Coulomb’s Law Physics 30 Outcome 1 Part 3: Coulomb’s Law Coulomb’s Law is an inverse square law that describes the force between two point charges: Example: What is the force on the +3.0 μC charge? Demo: Electric forces and gravitational forces Example: Suppose you hung two pith balls from long insulating strings of length 10 cm. You then touched the pith balls with a charged Teflon rod, causing them both to become equally charged. The pith balls are seen to repel each other and hang a distance d=2.5 m apart. The pass of each pith ball is 0.50 g. Determine the magnitude of the electric force on each ball and calculate the charge. Lesson 2: Coulomb’s Law Physics 30 Outcome 1 Part 4: Curve Straightening In a Coulomb-type experiment, students were investigating the relationship between the force of electrostatic repulsion acting on two charged spheres and their separation distance The results of their investigations yielded the following results. 1) Draw a graph of the results shown in the table. 2) From the shape of the graph, what is the relationship between the electrostatic force and the separation distance between two charges? 3) Make a new table of values to obtain data to straighten the graph (Curve Straightening) Fe = kq1q2 r2 !1" Fe = kq1q2 ⋅ $ 2 % &r ' you can compare this to y = m*x (equation of a line) where Fe is your y, (1/r2) is your x. 4) Draw a Graph of the data in your new table of values 5) Determine the slope of the graph 6) What does the slope of this graph represent? 7) If the charges of the two spheres are the same, what is the value of the charge on each sphere? Lesson 2: Coulomb’s Law Physics 30 Outcome 1 Part 5: Vectors and Vector Addition Vectors Scalars Vector notation: Magnitude [angle] notation (Alberta high school): Component notation (U of C first year): Unit vector notation: Example: Draw the force vector with a magnitude of 150 N at an angle of 30o north of east and write it in the three different notations. Example: A box is pushed along a road with a force of <13, -14> N. Convert this force vector into magnitude [angle] notation. Lesson 2: Coulomb’s Law Physics 30 Outcome 1 Vector Operations: Multiply by a scalar Example: A 10 kg box is pushed with an acceleration of 15 m/s2 [12o N of W]. What is the force on the box? Example: A car travels with a velocity of <15, -10> m/s for 15 s. What is the car’s displacement? Add two vectors Example: Add the force vectors F1 = 15 N [30o S of E] and F2 = 25 N [12o N of E] Note: you are not able to add a vector to a scalar or multiply to vectors using high school vector algebra. Part 6: Superposition of Electric Forces The Principle of Superposition for Coulomb's Law of Electric Force | Doc Physics The principle of superposition states that the interaction between any two charges is unaffected by the presence of others. In other words, if there are multiple charges in an area and you are interested in the total force on one of these charges, let’s call it qo, you can calculate the force between qo and each charge individually, ignoring the others, and then add the forces together. Physics 30 Outcome 1 Example: Calculate the net force on charge 3 Example: What is the net force on charge 2? Lesson 2: Coulomb’s Law Physics 30 Outcome 1 Example: What is the force on charge 3? Example: What is the force on charge 1? Lesson 2: Coulomb’s Law Lesson 2: Coulomb’s Law Physics 30 Outcome 1 LESSON 2 SUMMARY NOTES Name: ___________________________________ Hand in instructions: Take a picture or scan (using a scanning app) of this page when completed and submit the image file or pdf to the dropbox folder for Outcome 1 Summary Notes on D2L. Fill in everything you have learned about the following topics using your lesson 1 booklet Give the symbol and unit for charge Describe or draw Coulomb’s Torsion Balance Write the equation for Coulomb’s law and state the meaning and unit for each of the symbols in the equation What is the shape of an inverse square graph and how does this relate to Coulomb’s Law? Create a vector. Draw your vector as a vector diagram (triangle) and show it written in each of the three notations. Explain how to convert between the each of the three forms of vector notation. How do you add two vectors? Give an example What is the principle of superposition for electric force? Physics 30 Outcome 1 Lesson 2: Coulomb’s Law Lesson 2 Practice Problems 1. In a hydrogen atom, an electron is 5.29 x 10-11 m from a proton. An electron has a charge of -1.60 x 10-19 C, and the proton’s charge is +1.60 x 10-19 C. Calculate the electrostatic force of attraction acting on the two charges. [8.22 x 10-8 N [attraction]] 2. The electric force between two charged objects is 5.2 x 10-4 N when the objects are 3.11 x 10-1 m apart. What is the electric force between the same objects if the distance is changed to 4.04 x 10-1 m? (3.1 x 10-4 N) 3. Two small metallic spheres have the same mass and volume. One of the spheres has a charge of +4.00 μC and the other a charge of -1.00 μC. If the two spheres are brought into brief contact with each other and are then separated to a distance of 0.200 m, what is the electric force between them? (0.506 N) 4. Three charges are placed in a line, as shown in the diagram. a) What is the net electrostatic force on charge A? [1.20 x 104 N [right]] b) What is the net electrostatic force on charge B? [7.49 x 103 N [left]] 5. Calculate the net electrostatic force on charge B shown in the figure to the right. [2.54 x 102 N [225o]] 6. A metal sphere with a negative charge of 3.00 µC is placed 12.0 cm from another similar metal sphere with a positive charge of 2.00 µC. The two spheres momentarily touch, and then return to their original positions. Calculate the electrostatic force acting on the two metal spheres. [1.56 x 10-1 N [repulsion]] 7. A metal sphere with a charge of -2.50 x 10-9 C is 1.50 cm to the left of a second metal sphere with a charge of +1.50 x 10-9 C. A third metal sphere of -1.00 x 10-9 C is situated 2.00 cm to the right of the second charged sphere. If all three charges form a line, determine the net electrostatic force on the second sphere. [1.16 x 10-4 N [left]] 8. Two point charged objects produce an electric force of 0.0620 N on each other. What is the electric force if the distance between them increases three times and one of the charges is doubled? (0.0138 N) 9. From the diagram to the right determine the net electrostatic force on C. [16.8 N at 12.6o W of S] 10. In the diagram to the right, A has a charge of +0.30 μC, B has a charge of -0.20 μC and C has a charge of -0.20 μC. What is the net force on A? (0.093 N [S])