DAD-E Lab 1 Coulomb Force Study v2

DAD-E Lab 1: Coulomb Force Study [Do-At-Domicile - Electric] Submitted by: Nora Peterson Collaborators: Caitlyn Miller Identified as one of the basic forces, the Coulomb or Electrostatic force is responsible for much of chemical, and through that, biological, interactions. The Electric Force along with gravity are the two forces that account for most of our understanding of nature. Nuclear forces account for almost all of the rest. It is also of interest that the electric force, first described mathematically by Coulomb, and the universal gravitational force, first described mathematically by Newton, have the same mathematical structure, but with wildly different fundamental constants. To be more specific, consider two masses with charges ( m 1 ,q 1 ) , and ( m 2 ,q 2 ) where “m” is for mass and “q” is for charge. If they are separated by a distance of “r” then the magnitudes of the interacting forces between them are: For gravity: F G = G m 1 m 2 r 2 For the electric force: F E = k q 1 q 2 r 2 Notice how similar they look. However, while the gravitational force is always attractive, the electric force can be either attractive (for opposite charges) or repulsive (for similar charges), since charges can be either positive “+” or negative “-“. Another difference is the values of the constants “G” and “k” which are: G = 6.67 × 10 − 11 N ∙m 2 kg 2 k = 8.99 × 10 + 9 N ∙m 2 C 2 ≈ 9 × 10 + 9 N ∙m 2 C 2 The new thing is the unit of charge, the Coulomb or “C” which we may not have talked about before, but is necessary when dealing with charges, currents, and magnetic fields. It turns out all charges are integer multiples of the elementary charge, e = 1.6 × 10 − 19 C , that is charge is quantized. Exercise 1: To give an idea of the difference in the scale of these forces, let’s calculate them for a hydrogen atom, the simplest and most abundant atom in the universe. Hydrogen is composed of one electron and one proton. Both have the same magnitude of charge but different signs (+e, and –e). The proton mass is much larger than the electron mass, but they are the same distance apart. The values are: mass charge Distance (Bohr Radius) © Larry Browning, 2020

Proton m p = 1.67 × 10 − 27 kg + e =+ 1.6 × 10 − 19 C r B = 5.29 × 10 − 11 m Electron m e = 9.11 × 10 − 31 kg − e =− 1.6 × 10 − 19 C r B = 5.29 × 10 − 11 m Take some time in your teams to come up with these values and be ready to share your results with the class in a few minutes. F G = 3.63 x 10 − 47 N F E =− 8.22 x 10 − 8 Finally calculate the ratio: F E F G = ¿ 2.26 x 10 39 Exercise 2: Explore the Coulomb force with PhET simulation. Go to the PhET simulation at https://phet.colorado.edu/en/simulation/coulombs-law and start it in “Macro Scale.” Make sure the charges are at q 1 =− 4 µC and q 2 =+ 8 µC and that q 1 is all the way to the left (over zero) and that q 2 is centered over the 5 cm mark, as shown. Some things to observe and discuss: In which directions are the forces acting? Attractive How would you describe this? The two charges are opposite, so they are pulled toward each other. As q 1 is moved to the right, what happens to the magnitude of the forces? Their magnitudes increase. Move q 1 back to the origin. What is the magnitude of the force? 115.041 N Where is q 1 when that force doubles? 1.5 cm © Larry Browning, 2020

force has a magnitude of twice as much or 228 N? [Hint: look at the number in the spread sheet or measure the distance in the simulation by moving q 2 .] -3.55 cm What is the ratio of this distance to the original 5 cm distance? 0.71 What is the separation when the force has a magnitude four times as much or 456 N? -2.5 cm What is the ratio of this distance to the original 5 cm distance? 0.5 What is the separation when the force has a magnitude nine times as much or 1026 N? -1.65 cm What is the ratio of this distance to the original 5 cm distance? 0.33 How does F E = k q 1 q 2 r 2 quickly and easily predict these results? [Hint: Examine the ratio of the forces as functions when only the distances are different.] As the distance between the charges decreases, the force of attraction increases exponentially. If these are ideal point charges, is there any limit to how big the Coulomb force can be? No, when the distance between them is closest to 0, the force of attraction reaches infinity. © Larry Browning, 2020