Concept explainers
DATA The Millikan Oil-Drop Experiment. The charge of an electron was first measured by the American physicist Robert Millikan during 1909–1913. In his experiment, oil was sprayed in very fine drops (about 10−4 mm in diameter) into the space between two parallel horizontal plates separated by a distance d. A potential difference VAB was maintained between the plates, causing a downward electric field between them. Some of the oil drops acquired a negative charge because of frictional effects or because of ionization of the surrounding air by x rays or radioactivity. The drops were observed through a microscope, (a) Show that an oil drop of radius r at rest between the plates remained at rest if the magnitude of its charge was
where ρ is oil’s density. (Ignore the buoyant force of the air.) By adjusting VAB to keep a given drop at rest, Millikan determined the charge on that drop, provided its radius r was 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 υt of the drop as it fell. (We discussed terminal speed in Section 5.3.) The viscous force F on a sphere of radius r moving at speed υ through a fluid with viscosity η is given by Stokes’s law: F = 6πηrυ. When a drop fell at υt, the viscous force just balanced the drop’s weight w = mg. Show that the magnitude of the charge on the drop was
(c) You repeat the Millikan oil-drop experiment. Four of your measured values of VAB and υt are listed in the table:
In your apparatus, the separation d between the horizontal plates is 1.00 mm. The density of the oil you use is 824 kg/m3. For the viscosity η of air, use the value 1.81 × 10−4 N · s/m2. Assume that g = 9.80 m/s2. Calculate the charge q of each drop, (d) If electric charge is quantized (that is, exists in multiples of the magnitude of the charge of an electron), then the charge on each drop is −ne, where n is the number of excess electrons on each drop. (All four drops in your table have negative charge.) Drop 2 has the smallest magnitude of charge observed in the experiment, for all 300 drops on which measurements were made, so assume that its charge is due to an excess charge of one electron. Determine the number of excess electrons n for each of the other three drops, (e) Use q = −ne to calculate e from the data for each of the four drops, and average these four values to get your best experimental value of e.
Want to see the full answer?
Check out a sample textbook solutionChapter 23 Solutions
University Physics with Modern Physics (14th Edition)
Additional Science Textbook Solutions
Glencoe Physical Science 2012 Student Edition (Glencoe Science) (McGraw-Hill Education)
Tutorials in Introductory Physics
Lecture- Tutorials for Introductory Astronomy
Physics (5th Edition)
Modern Physics
Physics for Scientists and Engineers: A Strategic Approach, Vol. 1 (Chs 1-21) (4th Edition)
- A particle with charge 1.60 1019 C enters midway between two charged plates, one positive and the other negative. The initial velocity of the particle is parallel to the plates and along the midline between them (Fig. P26.48). A potential difference of 300.0 V is maintained between the two charged plates. If the lengths of the plates are 10.0 cm and they are separated by 2.00 cm, find the greatest initial velocity for which the particle will not be able to exit the region between the plates. The mass of the particle is 12.0 1024 kg. FIGURE P26.48arrow_forwardAir breaks down and conducts charge as a spark if the electric field magnitude exceeds 3.00 106 V/m. (a) Determine the maximum charge Qmax that can be stored on an air-filled parallel-plate capacitor with a plate area of 2.00 104 m2. (b) A 75.0 F air-filled parallel-plate capacitor stores charge Qmax. Find the potential difference across its plates.arrow_forwardAn election enters a region between two large parallel plates made of aluminum separated by a distance of 2.0 cm and kept at a potential difference of 200 V. The electron enters through a small hole in the negative plate and moves toward the positive plate. At the time the electron is near the negative plate, its speed is 4.0103 m/s. Assume the electric field between the plates to be uniform, and find the speed of electron at (a) 0.10 cm, (b) 0.50 cm, (c) 1.0 cm, and (d) 1.5 cm from the negative plate, and (e) immediately before it hits the positive plate.arrow_forward
- A spherical balloon contains a positively charged particle at its center. As the balloon is inflated to a larger volume while the charged particle remains at the center, which of the following are true? (a) The electric potential at the surface of the balloon increases. (b) The magnitude of the electric field at the surface of the balloon increases. (c) The electric flux through the balloon remains the same. (d) None of these.arrow_forwardA point charge of q=50108 C is placed at the center of an uncharged spherical conducting shell of inner radius 6.0 cm and outer radius 9.0 cm. Find the electric potential at (a) r = 4,0cm, (b) r = 8.0 cm, (c) r — 12.0 cm.arrow_forwardGiven two particles with 2.00-C charges as shown in Figure P20.9 and a particle with charge q = 1.28 1018 C at the origin, (a) what is the net force exerted by the two 2.00-C charges on the test charge q? (b) What is the electric field at the origin due to the two 2.00-C particles? (c) What is the electric potential at the origin due to the two 2.00-C particles? Figure P20.9arrow_forward
- A spherical balloon contains a positively charged particle at its center. As the balloon is inflated to a larger volume while the charged particle remains at the center, which of the following are true? (a) The electric potential at the surface of the balloon increases. (b) The magnitude of the electric field at the surface of the balloon increases. (c) The electric flux through the balloon remains the same. (d) None of these.arrow_forwardHow many electrons should be removed from an initially uncharged spherical conductor of radius 0.300 m to produce a potential of 7.50 kV at the surface?arrow_forwardWhen a potential difference of 150. V is applied to the plates of an air-filled parallel-plate capacitor, the plates carry a surface charge density of 3.00 1010 C/cm2. What is the spacing between the plates?arrow_forward
- A small spherical pith ball of radius 0.50 cm is painted with a silver paint and then -10 C of charge is placed on it. The charged pith ball is put at the center of a gold spherical shell of inner radius 2.0 cm and outer radius 2.2 cm. (a) Find the electric potential of the gold shell with respect to zero potential at infinity, (b) How much charge should you put on the gold shell if you want to make its potential 100 V?arrow_forwardA uniformly charged insulating rod of length 14.0 cm is bent into the shape of a semicircle as shown in Figure P20.29. The rod has a total charge of 7.50 C. Find the electric potential at O, the center of the semicircle. Figure P20.29arrow_forwardLightning can be studied with a Van de Graaff generator, which consists of a spherical dome on which charge is continuously deposited by a moving belt. Charge can be added until the electric field at the surface of the dome becomes equal to the dielectric strength of air. Any more charge leaks off in sparks as shown in Figure P20.67. Assume the dome has a diameter of 30.0 cm and is surrounded by dry air with a breakdown electric field of 3.00 106 V/m. (a) What is the maximum potential of the dome? (b) What is the maximum charge on the dome? Figure P20.67 David Evison/Shutterstock.comarrow_forward
- Physics for Scientists and Engineers: Foundations...PhysicsISBN:9781133939146Author:Katz, Debora M.Publisher:Cengage LearningCollege PhysicsPhysicsISBN:9781305952300Author:Raymond A. Serway, Chris VuillePublisher:Cengage Learning
- Principles of Physics: A Calculus-Based TextPhysicsISBN:9781133104261Author:Raymond A. Serway, John W. JewettPublisher:Cengage LearningCollege PhysicsPhysicsISBN:9781285737027Author:Raymond A. Serway, Chris VuillePublisher:Cengage LearningCollege PhysicsPhysicsISBN:9781938168000Author:Paul Peter Urone, Roger HinrichsPublisher:OpenStax College