Millikan's Oil Drop Experiment: How to Determine the Charge of an Electron

Updated on March 30, 2018
Sam Brind profile image

Sam Brind holds a master's in physics with theoretical physics (MPhys) from the University of Manchester.

The Discovery of the Electron's Charge

In 1897 J. J. Thomson demonstrated that cathode rays, a new phenomenon, were made up of small negatively charged particles, which were soon named electrons. The electron was the first subatomic particle ever discovered. Through his cathode ray experiments, Thomson also determined the electrical charge-to-mass ratio for the electron.

Millikan's oil-drop experiment was performed by Robert Millikan and Harvey Fletcher in 1909. It determined a precise value for the electric charge of the electron, e. The electron's charge is the fundamental unit of electric charge, because all electric charges are made up of groups (or the absence of groups) of electrons. This discretisation of charge is also elegantly demonstrated by Millikan's experiment.

The unit of electric charge is a fundamental physical constant and crucial to calculations within electromagnetism. Hence, an accurate determination of its value was a big achievement, recognised by the 1923 Nobel prize for physics.

Robert Millikan, the 1923 Nobel prize winning physicist, who determined the electron's charge
Robert Millikan, the 1923 Nobel prize winning physicist, who determined the electron's charge | Source

Millikan's Apparatus

Millikan's experiment is based around observing charged oil droplets in free fall and in the presence of an electric field. A fine mist of oil is sprayed across the top of a perspex cylinder with a small 'chimney' that leads down to the cell (if the cell valve is open). The act of spraying will charge some of the released oil droplets through friction with the nozzle of the sprayer. The cell is the area enclosed between two metal plates that are connected to a power supply. Hence an electric field can be generated within the cell and its strength varied by adjusting the power supply. A light is used to illuminate the cell and the experimenter can observe within the cell by looking through a microscope.

The apparatus used for Millikan's experiment (shown from two perspectives).
The apparatus used for Millikan's experiment (shown from two perspectives).

Terminal velocity

As an object falls through a fluid, such as air or water, the force of gravity will accelerate the object and speed it up. As a consequence of this increasing speed, the drag force acting on the object, that resists the falling, also increases. Eventually these forces will balance (along with a buoyancy force) and therefore the object no longer accelerates. At this point the object is falling at a constant speed, which is called the terminal velocity. The terminal velocity is the maximum speed the object will obtain while free falling through the fluid.


Millikan's experiment revolves around the motion of individual charged oil droplets within the cell. To understand this motion the forces acting on an individual oil droplet need to be considered. As the droplets are very small, the droplets are reasonably assumed to be spherical in shape. The diagram below shows the forces and their directions that act on a droplet in two scenarios: when the droplet free falls and when an electric field causes the droplet to rise.

The different forces acting on a oil drop falling through air (left) and rising through air due to an applied electric field (right).
The different forces acting on a oil drop falling through air (left) and rising through air due to an applied electric field (right).

The most obvious force is the gravitational pull of the Earth on the droplet, also known as the weight of the droplet. Weight is given by the droplet volume multiplied by the density of the oil (ρoil) multiplied by the gravitational acceleration (g). Earth's gravitational acceleration is known to be 9.81 m/s2 and the density of the oil is usually also known (or could be determined in another experiment). However, the radius of the droplet (r) is unknown and extremely hard to measure.

As the droplet is immersed in air (a fluid) it will experience an upward buoyancy force. Archimedes' principle states that this buoyancy force is equal to the weight of fluid displaced by the submerged object. Therefore, the buoyancy force acting on the droplet is an identical expression to the weight except the density of air is used (ρair). The density of air is a known value.

The droplet also experiences a drag force that opposes its motion. This is also called air resistance and occurs as a consequence of friction between the droplet and the surrounding air molecules. Drag is described by Stoke's law, which says that the force depends on the droplet radius, viscosity of air (η) and the velocity of the droplet (v). The viscosity of air is known and the droplet velocity is unknown but can be measured.

When the droplet reaches its terminal velocity for falling (v1), the weight is equal to the buoyancy force plus the drag force. Substituting the previous equations for the forces and then rearranging gives an expression for the droplet radius. This allows the radius to be calculated if v1 is measured.

When a voltage is applied to the brass plates an electric field is generated within the cell. The strength of this electric field (E) is simply the voltage (V) divided by the distance separating the two plates (d).

If a droplet is charged it will now experience an electrical force in addition to the three previously discussed forces. Negatively charged droplets will experience an upwards force. This electrical force is proportional to both the electric field strength and the droplet's electrical charge (q).

If the electric field is strong enough, from a high enough voltage, the negatively charged droplets will start to rise. When the droplet reaches its terminal velocity for rising (v2), the sum of the weight and drag is equal to the sum of the electrical force and the buoyancy force. Equating the formulae for these forces, substituting in the previously obtained radius (from the fall of the same droplet) and rearranging gives an equation for the droplet's electrical charge. This means that the charge of a droplet can be determined through measurement of the falling and rising terminal velocities, as the rest of the equation's terms are known constants.

Experimental Method

Firstly, calibration is performed such as focusing the microscope and ensuring the cell is level. The cell valve is opened, oil sprayed across the top of the cell and the valve is then closed. Multiple droplets of oil will now be falling through the cell. The power supply is then turned on (to a sufficiently high voltage). This causes negatively charged droplets to rise but also makes positively charged droplets fall quicker, clearing them from the cell. After a very short time this only leaves negatively charged droplets remaining in the cell.

The power supply is then turned off and the drops begin to fall. A droplet is selected by the observer, who is watching through the microscope. Within the cell, a set distance has been marked and the time for the selected droplet to fall through this distance is measured. These two values are used to calculate the falling terminal velocity. The power supply is then turned back on and the droplet begins to rise. The time to rise through the selected distance is measured and allows the rising terminal velocity to be calculated. This process could be repeated multiple times and allow average fall and rise times, and hence velocities, to be calculated. With the two terminal velocities obtained, the droplet's charge is calculated from the previous formula.


This method for calculating a droplet's charge was repeated for a large number of observed droplets. The charges were found to all be integer multiples (n) of a single number, a fundamental electric charge (e). Therefore, the experiment confirmed that charge is quantised.

A value for e was calculated for each droplet by dividing the calculated droplet charge by an assigned value for n. These values were then averaged to give a final measurement of e.

Millikan obtained a value of -1.5924 x 10-19 C, which is an excellent first measurement considering that the currently accepted measurement is -1.6022 x 10-19 C.

What Does This Look Like?

Questions & Answers

  • Why do we use oil and not water when determining the charge of an electron?

    Millikan needed a liquid to produce droplets that would maintain their mass and spherical shape throughout the course of the experiment. To allow the droplets to be clearly observed, a light source was used. Water was not a suitable choice as water droplets would have begun evaporating under the heat of the light source. Indeed, Millikan chose to use a special type of oil that had a very low vapor pressure and would not evaporate.

  • How was the value of 'n' calculated for the problem described in this article?

    After performing the experiment, a histogram of electrical charges from the observed droplets is plotted. This histogram should roughly show a pattern of equally spaced clusters of data (demonstrating a quantized charge). Droplets within the lowest value cluster are assigned an 'n' value of one, droplets within the next lowest value cluster are assigned an 'n' value of two and so on.

  • What is the acceleration of the droplet if the electric force is equal but opposite to that of gravity?

    If the electrical force exactly balances the force of gravity the oil droplet's acceleration will be zero, causing it to float in mid-air. This is actually an alternative to the method of observing the droplet rise in an electric field. However, it is much more difficult to realize these conditions and observe a floating droplet, as it will still be undergoing random motion as a result of collisions with air molecules.

  • How do the oil droplets acquire either the negative or the positive charge?

    The electrical charge of the oil droplets is a convenient byproduct of how the oil is inserted into the cell. Oil is sprayed into the tube, during this spraying process some of the droplets will obtain a charge through friction with the nozzle (similar to the effect of rubbing a balloon on your head). Alternatively, the droplets could be given a charge by exposing the droplets to ionizing radiation.

© 2017 Sam Brind


    0 of 8192 characters used
    Post Comment
    • profile image

      Nwizzi chinwendu 

      5 months ago

      The best explanation

    • profile image

      Wafula Eric 

      6 months ago

      Thanks for this well-detailed explanation. I really adored it

    • profile image


      8 months ago

      One of the best explanation to the topic.

      Detailed and most importantly well structured and presented.

    • profile image

      paul chukwualuka 

      9 months ago

      quite elaborate and detailed

    • profile image

      samuel mutukiu 

      12 months ago

      its a wonderful explanation .The basis of Millikan's experiment is openly understood.

    • profile image


      16 months ago

      It is a beautiful introduction about oil drop experiment. From background, theory to data analyses, it is quite clear.

    • Sam Brind profile imageAUTHOR

      Sam Brind 

      16 months ago

      Like all other scientific experiments, the quantities involved are measured in SI units. For example: masses are measured in kilograms (kg), distances are measured in metres (m), forces are measured in Newtons (N) and electrical charges are measured in Coulombs (C).

    • profile image

      ASE DAVID Alabokurogha 

      16 months ago

      good one but I still

      need to know the basic units

    • profile image

      professor kasirye 

      21 months ago

      this is really wonderful, I just liked it's simplicity


    This website uses cookies

    As a user in the EEA, your approval is needed on a few things. To provide a better website experience, uses cookies (and other similar technologies) and may collect, process, and share personal data. Please choose which areas of our service you consent to our doing so.

    For more information on managing or withdrawing consents and how we handle data, visit our Privacy Policy at:

    Show Details
    HubPages Device IDThis is used to identify particular browsers or devices when the access the service, and is used for security reasons.
    LoginThis is necessary to sign in to the HubPages Service.
    Google RecaptchaThis is used to prevent bots and spam. (Privacy Policy)
    AkismetThis is used to detect comment spam. (Privacy Policy)
    HubPages Google AnalyticsThis is used to provide data on traffic to our website, all personally identifyable data is anonymized. (Privacy Policy)
    HubPages Traffic PixelThis is used to collect data on traffic to articles and other pages on our site. Unless you are signed in to a HubPages account, all personally identifiable information is anonymized.
    Amazon Web ServicesThis is a cloud services platform that we used to host our service. (Privacy Policy)
    CloudflareThis is a cloud CDN service that we use to efficiently deliver files required for our service to operate such as javascript, cascading style sheets, images, and videos. (Privacy Policy)
    Google Hosted LibrariesJavascript software libraries such as jQuery are loaded at endpoints on the or domains, for performance and efficiency reasons. (Privacy Policy)
    Google Custom SearchThis is feature allows you to search the site. (Privacy Policy)
    Google MapsSome articles have Google Maps embedded in them. (Privacy Policy)
    Google ChartsThis is used to display charts and graphs on articles and the author center. (Privacy Policy)
    Google AdSense Host APIThis service allows you to sign up for or associate a Google AdSense account with HubPages, so that you can earn money from ads on your articles. No data is shared unless you engage with this feature. (Privacy Policy)
    Google YouTubeSome articles have YouTube videos embedded in them. (Privacy Policy)
    VimeoSome articles have Vimeo videos embedded in them. (Privacy Policy)
    PaypalThis is used for a registered author who enrolls in the HubPages Earnings program and requests to be paid via PayPal. No data is shared with Paypal unless you engage with this feature. (Privacy Policy)
    Facebook LoginYou can use this to streamline signing up for, or signing in to your Hubpages account. No data is shared with Facebook unless you engage with this feature. (Privacy Policy)
    MavenThis supports the Maven widget and search functionality. (Privacy Policy)
    Google AdSenseThis is an ad network. (Privacy Policy)
    Google DoubleClickGoogle provides ad serving technology and runs an ad network. (Privacy Policy)
    Index ExchangeThis is an ad network. (Privacy Policy)
    SovrnThis is an ad network. (Privacy Policy)
    Facebook AdsThis is an ad network. (Privacy Policy)
    Amazon Unified Ad MarketplaceThis is an ad network. (Privacy Policy)
    AppNexusThis is an ad network. (Privacy Policy)
    OpenxThis is an ad network. (Privacy Policy)
    Rubicon ProjectThis is an ad network. (Privacy Policy)
    TripleLiftThis is an ad network. (Privacy Policy)
    Say MediaWe partner with Say Media to deliver ad campaigns on our sites. (Privacy Policy)
    Remarketing PixelsWe may use remarketing pixels from advertising networks such as Google AdWords, Bing Ads, and Facebook in order to advertise the HubPages Service to people that have visited our sites.
    Conversion Tracking PixelsWe may use conversion tracking pixels from advertising networks such as Google AdWords, Bing Ads, and Facebook in order to identify when an advertisement has successfully resulted in the desired action, such as signing up for the HubPages Service or publishing an article on the HubPages Service.
    Author Google AnalyticsThis is used to provide traffic data and reports to the authors of articles on the HubPages Service. (Privacy Policy)
    ComscoreComScore is a media measurement and analytics company providing marketing data and analytics to enterprises, media and advertising agencies, and publishers. Non-consent will result in ComScore only processing obfuscated personal data. (Privacy Policy)
    Amazon Tracking PixelSome articles display amazon products as part of the Amazon Affiliate program, this pixel provides traffic statistics for those products (Privacy Policy)
    ClickscoThis is a data management platform studying reader behavior (Privacy Policy)