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In this problem, we will go through the famous experiment led by Robert A. Millikan. The charge of electron that he calculated by this experiment is 0.6% off from the currently accepted value, that too due to the 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 v_d. Eq mg Now, we negatively charge the oil droplet and place it in between the charged plates. There is a voltage V = 9.31Volt between the plates and the separation between the plates is d = 1.94mm. Previously we have seen the droplet 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.

In this problem, we will go through the famous experiment led by Robert A. Millikan. The charge of electron that he calculated by this experiment is 0.6% off from the currently accepted value, that too due to the 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 v_d. Eq mg Now, we negatively charge the oil droplet and place it in between the charged plates. There is a voltage V = 9.31Volt between the plates and the separation between the plates is d = 1.94mm. Previously we have seen the droplet 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.

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Please solve a,b & c.
In this problem, we will go through the famous experiment led by Robert A. Millikan. The charge of electron that he calculated by this experiment is 0.6% off from the currently accepted value, that too due to the 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 v_d. + Eq mg Now, we negatively charge the oil droplet and place it in between the charged plates. There is a voltage V = 9.31Volt between the plates and the separation between the plates is d = 1.94mm. Previously we have seen the droplet 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.
Transcribed Image Text:In this problem, we will go through the famous experiment led by Robert A. Millikan. The charge of electron that he calculated by this experiment is 0.6% off from the currently accepted value, that too due to the 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 v_d. + Eq mg Now, we negatively charge the oil droplet and place it in between the charged plates. There is a voltage V = 9.31Volt between the plates and the separation between the plates is d = 1.94mm. Previously we have seen the droplet 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, acceleration due to gravity g, upward terminal velocity of the droplet v_u, downward terminal velocity of the droplet v_d, potential difference V, separation between the plates d. 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. a) Write the mathematical expression for charge q. To proceed 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 Fd 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 coefficient is denoted by n, terminal velocity by vu , radius of the spherical droplet a and the density of oil p - the viscous drag force is given by :- Fd=6xTTxaxnxvu . In equilibrium, Fg-Fd - from which Millikan was able to calculate the radius of the oil droplet using the known values of air viscous coeffcient and the density of oil. In our problem, we are given the radius a=0.4µm found from the experimental procedure described here. The density of the oil is p=824kgm^-3. We have to calculate the mass of the oil droplet. We found that the mass of the oil droplet is 2.20*10^-16 Kg. Now, we can calculate the charge using the equation in no. (a). Because the value of velocity of the droplet (~10^-5 ) is very small compared to the values of other parameters, we make the approximation vd+vu=vd in the numerator of equation in no. (a). b) Find the charge of the oil droplet. ( Provide answer in the unit 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 integer multiple of an electron charge. Consider the numerical value of electron charge 1.6x10^-19 without the sign. c) Find the integer multiple of an electron charge for the charge of the oil droplet.
Transcribed Image Text:Use the symbolic expression for the mass of the oil droplet m, acceleration due to gravity g, upward terminal velocity of the droplet v_u, downward terminal velocity of the droplet v_d, potential difference V, separation between the plates d. 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. a) Write the mathematical expression for charge q. To proceed 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 Fd 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 coefficient is denoted by n, terminal velocity by vu , radius of the spherical droplet a and the density of oil p - the viscous drag force is given by :- Fd=6xTTxaxnxvu . In equilibrium, Fg-Fd - from which Millikan was able to calculate the radius of the oil droplet using the known values of air viscous coeffcient and the density of oil. In our problem, we are given the radius a=0.4µm found from the experimental procedure described here. The density of the oil is p=824kgm^-3. We have to calculate the mass of the oil droplet. We found that the mass of the oil droplet is 2.20*10^-16 Kg. Now, we can calculate the charge using the equation in no. (a). Because the value of velocity of the droplet (~10^-5 ) is very small compared to the values of other parameters, we make the approximation vd+vu=vd in the numerator of equation in no. (a). b) Find the charge of the oil droplet. ( Provide answer in the unit 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 integer multiple of an electron charge. Consider the numerical value of electron charge 1.6x10^-19 without the sign. c) Find the integer multiple of an electron charge for the charge of the oil droplet.
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