GA3.1 In this problem, we will go through the famous experiment led by Robert A. Millikan. The charge of elctron that he calculated by this experiment is 0.6% off from the currently accepted value, that too due to imprecise value of viscosity of air known at the time. This experiment demonstrates that the electric charge of the oil droplet is some integer multiple of electron charge - thereby establishing charge quantization as an experimental fact. mg It's a free body diagram. Here, we depict an oil droplet that is falling downwards due to gravity in an air medium. The droplet experiences an upward force due to air friction. When the two forces on the droplet balance, the droplet falls steadily with velocity va. Find the friction coeffcient k. Given the symbolic expression for the mass of the oil droplet m accelaration due to gravity g downward terminal velocity of the droplet v . Give your answer in terms of these variables. Use * to denote product and / to denote division. So to group the product of, say, a and b_1 write a*b_1. And to write a ratio of say, c_1 and d write c_1/d. To add the product and ratio write a*b_1 + c_1/d. If there are multiple products in the denominator, you should use brackets e.g. : (b_1 + c_1)/(a_1 * d). a) Write the mathematical expression for the friction coefficient k. k = Eg mg Now, we negatively charge the oil droplet and place it in between the charged plates. There is a voltage V = 10.12 Volt between the plates and the separation between the plates is d = 2.85 mm. Previously we have seen the droplet was steadily falling downwards. Now, due to the electric force on the droplet, it starts to move upwards, towards the positive plate. Hence, there's a force downwards on the droplet due to the air friction, as we can see from the free body diagram above. When all the forces acting on the droplet balance, the droplet steadily moves upwards. Use the symbolic expression for the mass of the oil droplet m, accelaration due to gravity g, upward terminal velocity of the droplet vu, downward terminal velocity of the droplet vd, potential difference V, separation between the plates d. Give your answer in terms of these variables. Use to denote product and / to denote division. So to group the product of, say, a and b_1 write a*b_1. And to write a ratio of say, c_1 and d write c_1/d. To add the product and ratio write a*b_1 + c_1/d. b)Write the mathematical expression for charge q. q = To procceed further, we need to know the mass of the oil droplet. So, Millikan turned off the electric field by taking the plates away. Hence, the droplet falls freely due to gravity. The viscous drag force Fa due to the air acts on the droplet against its weight Fg. The droplet soon reaches the terminal velocity when the forces balance. Stoke's law gives the drag force on the spherical droplet as it moves with the terminal velocity in air. If the viscous coeffcient is denoted by 7, terminal velocity by vy, radius of the spherical droplet a and the density of oil p - the viscous drag force is given by :- Fa = 6 x T X a ×n x Vq. In equilibrium, F, = Fa - from which Millikan was able to calculate the radius of the oil droplet using the known values of 0.4 um found from the experimental procedure described here. air viscous coeffcient and the density of oil. In our problem, we are given the radius a = The density of the oil is p = 824 kgm3. We have to calculate the mass of the oil droplet. c) Find the mass of the oil droplet. mass Give your answer up to at least three significance digits. kg Now, we can calculate the charge using the equation in (b). Because the value of velocity of the droplet (~ 10-5) is very small compared to the values of other parameters, we make the approximation va + vụ ~ Và in the numerator of equation in (b). d) Find the charge of the oil droplet. charge Give your answer up to at least three significance digits. C Now, we have the charge of the droplet. To test the charge quantization hypothesis, we'll have to consider the charge of the oil droplet is some interger multiple of an electron charge. Consider the numerical value of electron charge 1.6 x 1019 without the sign. e) Find the interger multiple of an electron charge for the charge of the oil droplet. integer Why is the charge quantized? - is a question pondered by the British Physicist Paul Dirac. He showed that the existence of a single magnetic monopole is sufficient for the quantization of electric charge. Till this day, no magnetic monopoles have been found. P. S.: There exist subatomic particles that are fractional multiples of electron charge. They are known as quarks. Quarks make up the proton and neutron. Quarks are never seen isolated due to a phenomena known as Quark Confinement. +