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The Milikan Oil-Drop Experiment. The charge of an electron was first measured by the American physicist Robert Millikan during $1909-1913$ . In his experiment, oil is sprayed in very fine drops (around $10^{-4} \mathrm{mm}$ in diameter) into the space between two parallel horizontal plates separated by a distance $d$ . A potential difference $V_{A B}$ is maintained between the parallel plates, causing a downward electric field between them. Some of the oil drops acquire a negative charge because of frictional effects or because of ionization of the surrounding air by $\mathrm{x}$ rays or radio- activity. The drops are observed through a microscope. (a) Show that an oil drop of radius $r$ at rest between the plates will remain at rest if the magnitude of its charge is $$ q=\frac{4 \pi \rho r^{3} g d}{3 V_{A B}} $$ where $\rho$ is the density of the oil. (Ignore the buoyant force of the air.) By adjusting $V_{A B}$ to keep a given drop at rest, the charge of on that drop can be determined, provided its radius is known. (b) Millikan's oil drops were much too small to measure their radii directly. Instead, Millikan determined $r$ by cutting off the electric field and measuring the terminal speed $v_{1}$ of the drop as it fell. (We $$ q=18 \pi \frac{d}{V_{A B}} \sqrt{\frac{\eta^{3} v_{1}^{3}}{2 \rho g}} $$

Name: Problem 91, Chapter 23: University Physics with Modern Physics
Uploaded: 2020-08-28T15:22:33-08:00
Duration: 8 min 10 s
Channel: Khoobchandra Agrawal

   The Milikan Oil-Drop Experiment. The charge of an electron was first measured by the American physicist Robert Millikan during $1909-1913$ . In his experiment, oil is sprayed in very fine drops (around $10^{-4} \mathrm{mm}$ in diameter) into the space between two parallel horizontal plates separated by a distance $d$ . A potential difference $V_{A B}$ is maintained between the parallel plates, causing a downward electric field between them. Some of the oil drops acquire a negative charge because of frictional effects or because of ionization of the surrounding air by $\mathrm{x}$ rays or radio- activity. The drops are observed through a microscope. (a) Show that an oil drop of radius $r$ at rest between the plates will remain at rest if the magnitude of its charge is $$ q=\frac{4 \pi \rho r^{3} g d}{3 V_{A B}} $$ where $\rho$ is the density of the oil. (Ignore the buoyant force of the air.) By adjusting $V_{A B}$ to keep a given drop at rest, the charge of on that drop can be determined, provided its radius is known. (b) Millikan's oil drops were much too small to measure their radii directly. Instead, Millikan determined $r$ by cutting off the electric field and measuring the terminal speed $v_{1}$ of the drop as it fell. (We $$ q=18 \pi \frac{d}{V_{A B}} \sqrt{\frac{\eta^{3} v_{1}^{3}}{2 \rho g}} $$

University Physics with Modern Physics

Hugh D. Young, Roger… 12th Edition

Chapter 23, Problem 91

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Solved by Expert Khoobchandra Agrawal

08/28/2020

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The gravitational force is given by $F_{g}=mg$ where $m$ is the mass of the oil drop and $g$ is the acceleration due to gravity. The electric force is given by $F_{e}=qE$ where $q$ is the charge on the oil drop and $E$ is the electric field between the plates. The Show more…

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The Milikan Oil-Drop Experiment. The charge of an electron was first measured by the American physicist Robert Millikan during $1909-1913$ . In his experiment, oil is sprayed in very fine drops (around $10^{-4} \mathrm{mm}$ in diameter) into the space between two parallel horizontal plates separated by a distance $d$ . A potential difference $V_{A B}$ is maintained between the parallel plates, causing a downward electric field between them. Some of the oil drops acquire a negative charge because of frictional effects or because of ionization of the surrounding air by $\mathrm{x}$ rays or radio- activity. The drops are observed through a microscope. (a) Show that an oil drop of radius $r$ at rest between the plates will remain at rest if the magnitude of its charge is $$ q=\frac{4 \pi \rho r^{3} g d}{3 V_{A B}} $$ where $\rho$ is the density of the oil. (Ignore the buoyant force of the air.) By adjusting $V_{A B}$ to keep a given drop at rest, the charge of on that drop can be determined, provided its radius is known. (b) Millikan's oil drops were much too small to measure their radii directly. Instead, Millikan determined $r$ by cutting off the electric field and measuring the terminal speed $v_{1}$ of the drop as it fell. (We $$ q=18 \pi \frac{d}{V_{A B}} \sqrt{\frac{\eta^{3} v_{1}^{3}}{2 \rho g}} $$

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Key Concepts

Stokes' Law

Stokes' law quantifies the viscous drag force experienced by small spherical objects moving through a fluid at low Reynolds numbers. It relates the drag force to the radius of the sphere, the velocity at which it moves, and the viscosity of the fluid, making it a fundamental tool for analyzing experiments involving terminal velocity measurements.

Viscous Drag and Terminal Velocity

When a small droplet falls through a fluid, it experiences a drag force due to the viscosity of the medium. As the droplet accelerates under gravity, it eventually reaches a terminal velocity where the drag force balances the gravitational force, ensuring constant speed. This behavior is essential for determining physical properties like radius indirectly.

Indirect Measurement Techniques

In situations where direct measurement is challenging or impossible, indirect methods are employed. For example, in the oil drop experiment, the drop's radius is not measured directly but is inferred from its terminal velocity. This approach leverages known relationships, like those provided by Stokes' law, to extract otherwise inaccessible physical parameters.

Electric Force Equilibrium

This concept involves balancing the different forces acting on an object so that the net force is zero, resulting in the object remaining at rest or moving at constant velocity. In experiments like the oil drop, the gravitational force pulling the droplet downward is balanced by the upward electric force when the droplet is suspended, illustrating the principle of force equilibrium in physics.

Electric Field and Potential Difference

An electric field is established by applying a potential difference across two plates, which creates a uniform field in the region between them. This field exerts a force on charged particles proportional to the magnitude of their charge, making it a crucial factor in experiments that measure the charge, such as the oil-drop experiment.

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Transcript

00:01 Hello friends, this problem is based on milliken's oil drop experiment.

00:09 Milken was a scientist who had first time measured the charge on the electron.

00:14 He had allowed the oil drop passing through the nozzle of atomizers so that due to friction of it it will get the charge due to transfer of electron and it is allowed to pass through the charge conducting plates having the uniform electric field.

00:35 And by finding the condition of rest or motion with terminality, he had calculated the charge on the electron.

00:44 So in the first case, we have to find the charge on the drop of radius are if drop is at rest.

01:02 Between the plates, drop will be at rest if it is in equilibrium.

01:08 That is weight of the drop is balanced by force due to electric fee.

01:16 So at equilibrium qe will be equal to mg.

01:30 So charge of the drop we will get mg upon e.

01:36 M is the mass of the drop which is measured volume of the drop into its density into g divided by electric field.

01:48 Electric field is potential difference between the plates and the distance between the plates.

01:54 So charge on the drop we will get 4 pi.

01:59 R cube row into d divided by three into potential difference so this is the answer of part a of this problem now in the part b radius of the drop is measured by measuring the terminal velocity if electric field is to be switched off then drop is moving under gravity under gravity and acquits terminable velocity.

03:08 If drop acquits the terminal velocity, then net force on it becomes zero...

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