PHY 1971 Coulombs Law Lab Report

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1 Coulomb’s Law Purpose The purpose of this lab is to explore the force pairs created by the interaction of electrical charges, and the inverse square nature of those forces. Theory Charles Coulomb, in 1785, experimentally determined the behavior of the physical interaction between two electrical charges. He found that any two electrical charges exert forces on each other that conform to the following rules: 1. The force is directed along a straight line between the two charges. 2. The magnitude of the forces is inversely proportional to the square of the distance between the centers of the two charges. 3. The magnitude of the forces is proportional to the product of the absolute values of the two charges. 4. The force is attractive if the two charges have opposite signs, and repulsive if the two charges have the same signs. These rules are quantified via the following equation known as Coulomb’s Law. 𝐹 = 𝑘 |𝑞 ଵ ||𝑞 ଶ | 𝑟 ଶ Here q 1 and q 2 are the charges, r is the distance between their centers, and k is known as Coulomb’s Constant with a value of k = 8.99·10 9 Nm 2 /C 2 . As already stated, when the charges have different signs the forces are attractive, meaning the forces are trying to pull each charge towards the other. When the charges have the same signs, the forces are repulsive, meaning they are trying to push the two charges away from each other.

2 Setup 1. Go to the following website: https://phet.colorado.edu/en/simulation/coulombs-law 2. You should now see the following: 3. Click on download and open the software when completed. 4. You should now see the following: 5. Double click the Macro Scale, the option on the left. 6. You should now see the following:

3 Procedure 1. In the grey box to the left of the bottom of your screen set charge 1 to, q 1 = - 10 µC. a. Record this value as -10.0 μC at the top of the Table. 2. In the grey box near the bottom and center of your screen set charge 2 to, q 2 = 10 µC. a. Record this value A 10.0 μc at the top of the Table. 3. In the grey box to the right of the bottom of your screen ‘check’ Force Values. 4. The position of the two charges is to be measured from the black dot at each of their centers. a. Move the charge on the left, q 1 , to position 0.00 cm. b. Move the charge on the right, q 2 , to position 10.00 cm 5. Record the value of the force acting on the charges in the Table for r = 10.00 cm, be sure to watch the precision (decimal places) when recording the Force data. a. Move the charges, and then record the force values for the rest of the values for r in the Table.

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4 Coulomb’s Law Online Lab Name Melissa Fernandez Ayala Course and section PHY 1971 - 009 Instructor Robert D. Hamby/Christopher Dunn Table : q 1 -10.0 μC q 2 10.0 μc (20 points) r (cm) F (N) 10.00 cm 89.876 N 9.00 cm 110.957 N 8.00 cm 140.430 N 7.00 cm 183.419 N 6.00 cm 249.654 N 5.00 cm 359.502 N 4.00 cm 561.722 N 3.00 cm 998.617 N 2.00 cm 2246.888 N 1.40 cm 4585.485 N 1. For both r = 10.00 cm, and r = 1.40 cm calculate the value for the electrostatic force . Show Sample Calculations (Formula and units). (10 points)

5 2. What direction does the force vector on q 1 point in? Make a simple sketch. (5 points) The force vector on q1 points toward the right, it is attracted to q2 3. What direction does the force vector on q 2 point in? Make a simple sketch. (5 points) The force vector on q2 points toward the left, it is attracted to q1 4. Why do those force vectors point in the directions they do? (10 points) The force vectors point in these directions because they are attractive forces ; charge q1 (negative) attracts charge q2 while q2 (positive) attracts charge q1. 5. If the charge on q 1 was positive, what direction would the force vector acting on it point? Make a simple sketch. (5 points) The force vector acting on the charge on q1 would point toward the left if its charge was positive because it would develop a repulsive force against the charge on q2.

6 6. If the charge on q 2 was negative, what direction would the force vector acting on it point? Make a simple sketch. (5 points) The force vector acting on the charge on q2 would point toward the right if its charge was positive because it would develop a repulsive force against the charge on q1. 7. Using Excel or some other graphing software make a graph of F vs r , with r in meters . Turn this graph in with your lab worksheet. Insert the graph below or attach it to the end of the worksheet. (10 points). 8. What happens to the value of F as r gets larger ? (5 points) As we know, the Coulombs law states that the force between two-point charges is directly proportional to the product of their charges and inversely proportional to the square of the distance between their centers. Essentially, the relationship on this graph is characterized by an inverse square law, specifically this graph shows a decreasing inverse square law. If the distance (r) between two-point charges increased, the force between would decrease, as depicted. This can be further defended via the formula: 𝐹 = ௞௤ భ ௤ మ ௥ మ . As the separation distance (r) increases, then the denominator r 2 becomes larger, and since the force is inversely proportional to this value, it will decrease.

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7 9. What happens to the value of F as r gets smaller ? (5 points) With respect to Coulomb's Law, the force between two-point charges will increase as their separation distance (r) decreases. To further prove this, the formula: 𝐹 = ௞௤ భ ௤ మ ௥ మ allows one to see that as the denominator of r 2 gets smaller, the overall product of the Force will become larger. Essentially, since it is inversely proportional to the square of the distance, the force (F) will increase. Conceptually this entails that the electrostatic force will become stronger as the charges move closer. As per the graph, it would show a rapid exponential increase rather than the decrease depicted in the graph from the PHET lab. Essentially the graph would be showing an inverse square relationship like before but in the opposite direction (upward). 10. Why does the graph have the shape it does? (20 points) The graph shows a decreasing inverse square law (or an exponential decrease/decay curve). As stated in the prior questions, we must relate the shape of the graph to Coulombs Law, which describes the electrostatic force between two charged particles. The relationship between force (F) and distance (r) can be expressed using 𝐹 = ௞௤ భ ௤ మ ௥ మ , the variables may be described as: F = electrostatic force between the two charges, k = Coulombs constant (8.99E9 Nm 2 /C 2 ), q1 and q2 = magnitudes of the charges, r = separation distance between the charges. On the graph, there is an exponential decay because as the distance between the charges (r) increases, the force (F) decreases. With the equation it is proven that as the denominator r 2 increases, the product of force will decrease. This can be explained physically as a reflection of the nature of electric charges, which exert a force on one another which gradually decreases with distance.

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