Polarization and Drift Speed
Claimed by Stephanie Tang (Stang76)
When looking at the polarization of conductors, drift speed is an important concept to consider as the conductor reaches equilibrium.
The Main Idea
Polarization is the process of the separation of opposite charges within an object. Drift speed is the speed at which mobile charges move through a conductor. When an object reaches equilibrium after polarization, the average drift speed of mobile charges in the conductor is zero.
Properties of Atoms
In all atoms, there are positively-charged particles called protons and negatively-charged particles called electrons. While the protons are tightly bound to the nucleus and restricted from movement, electrons are found in a general region around the nucleus called the electron cloud and are loosely bound. If a conductor is placed near a charged object, these electrons can even be induced to move to a different location within the object.
Polarization of Conductors and Insulators
Polarization is the process of the separation of opposite charges within an object. The process itself usually involves the utilization of a charged object to induce the movement of electrons. The charged object will give on an "applied electric field" that will affect particles within objects depending on the type of material it is.
Conductors are materials that have some kind of charged particle that can move freely across large distances throughout the object. A common example is simply a conducting metal. Because charged particles in conductors have the ability to travel large distances when subject to an applied electric field, the drift speed of these particles is crucial to understanding the relationship between polarization, drift speed, and equilibrium.
Insulators are materials with electrons firmly bound to atoms or molecules. As a result, these electrons and nuclei can only move small distances within the object. When insulators are polarized by an applied electric field, the individual molecules polarize according to the distance they are from the field and the strength of the field itself. This induced polarization results in many induced dipoles within the insulator. Drift speed is not considered with the polarization of insulators.
Drift Speed
Drift speed is the speed at which mobile charges move through a conductor. This quantity is directly proportional to net electric field and a proportionality constant called the mobility of the mobile charges. Different metals have different electron mobilities where the electron mobility is directly proportional to the drift speed. The direction drift velocity changes depending on the charge. For electrons, drift speed is in the opposite direction of the electric field while for proton, drift speed is in the same direction of the electric field.
To calculate drift speed: [math]\displaystyle{ \ v = u {E}_{net} }[/math] Where v is the average drift speed of a mobile charged particle, u is the mobility of the mobile charges, and [math]\displaystyle{ {E}_{net} }[/math] is simply the magnitude of the net electric field.
Drift speed is also important when looking at conventional current in a circuit. [math]\displaystyle{ \ I = |q| n A u E }[/math] or [math]\displaystyle{ \ I = |q| n A v }[/math]
Equilibrium
Equilibrium, specifically for conductors, is defined as the state of having no internal net electric field and no net movement of charges in any direction or in other words an average drift speed of zero.
Conditions for Equilibrium:
[math]\displaystyle{ v = 0 }[/math] and [math]\displaystyle{ {E}_{net} = 0 }[/math]
Examples
These examples are emphasized by the Matter and Interactions textbook.
Ionic Solutions
A good example of a conductor is an ionic solution with mobile charged particles, often cations and anions such as Na^+ and Cl^- in a salt water solution. In the presence of an applied electric field, a force will be applied on these charged particles to move according to their charge.
To determine the direction of movement: [math]\displaystyle{ \vec{F}_{net} = q \vec{E}_{net} }[/math]
Positively charged particles or cations will result in a positive force, meaning they move in the same direction as the applied electric field. Negatively charge particles or anions will result in a negative force, meaning they move in the opposite direction of the applied electric field.
The buildup of charges on opposite sides of the conductor caused by their movement from the applied electric field results in the creation of another electric field that counteracts the original applied field. Net electric field in this case is determined by the superposition of the external applied field and the internal electric field caused by polarization.
The process of polarization is rapid but not instantaneous. As long as [math]\displaystyle{ {E}_{net} }[/math] is not zero, the drift speed of the ions will not be zero and continue to build up, increasing the polarized electric field. Eventually, the conductor will reach equilibrium at the microscopic level or in other words have no net flow of mobile charges in any direction. [math]\displaystyle{ {E}_{net} }[/math] and the drift speed are now both zero. This is the definition of a conductor in equilibrium.
Things to consider:
There must be a constant applied electric field to have a constant speed of movement of ions.
The ions will not keep accelerating forever.
There is no net interaction between mobile electrons. The repulsion of electrons is neutralized by the attraction from the positive atomic cores. To know more about electron motion, read about the Drude Model describing the acceleration and energy of a mobile electron in a metal.
The Human Body
The human body itself is mostly composed of salt water. As a result, external charges can polarize individual molecules inside your body, shifting ion concentration in blood and tissues!
Homework Problem
Given as Checkpoint 6 in section 14.5 of the Matters and Interactions textbook:
An electric field of magnitude 190 N/C is applied to a solution containing chloride ions. The mobility of chloride ions in solution is 7.91e-8 (m/s)/(N/C). What is the average drift speed of the chloride ions in the solution?
[math]\displaystyle{ \ v = u {E}_{net} }[/math]
[math]\displaystyle{ \ v = (7.91e-8)*(190) }[/math]
[math]\displaystyle{ \ v = 1.5029e-5 m/s }[/math]
Taken from a WebAssign problem in Homework Week 3:
An electric field is applied to a solution containing bromide ions. As a result, the ions move through the solution with an average drift speed of 6.2e−7 m/s. The mobility of bromide ions in solution is 8.1e−8 (m/s)/(N/C). What is the magnitude of the net electric field inside the solution?
[math]\displaystyle{ \ v = u {E}_{net} }[/math]
[math]\displaystyle{ \ (6.2e−7) = (8.1e−8 )*(E) }[/math]
[math]\displaystyle{ \ E = 7.654 N/C }[/math]
A Computational Model
To visualize this concept, images are sufficient enough to convey the major points. There were no specific Physics 2212 labs dealing with vPython and drift speed in conductors.
Connectedness
- Physics is prevalent in many areas of life in terms of polarization and drift speed, as shown through the example of the human body being a large conductor.
- Industrial Systems and Engineering does not have much overlap with physics with the exception of certain concentrations that may require knowledge of physics. As of now, there is no direct application to my major.
- Drift speed and electron mobility are important in other concepts such as scattering, Hall effect, and doping elements.
History
There is no specific historical context associated with drift speed and polarization.
See also
Further reading
Matter and Interactions Volume II Chapter 14 Sections 14.3-14.6
http://www.physicsbook.gatech.edu/Polarization
http://www.physicsbook.gatech.edu/Polarization_of_an_Atom
http://www.physicsbook.gatech.edu/Charged_Conductor_and_Charged_Insulator
http://www.physicsbook.gatech.edu/Charge_Motion_in_Metals
External links
For lecture videos on the topic: [1]
For more information on the relationship between current and drift velocity: [2]
For an in-depth explanation of the Drude Model on electron motion: [3]
References
Chabay, Ruth W., and Bruce A. Sherwood. Matter and Interactions: Electric and Magnetic Interactions Fourth Edition. Hoboken: North Carolina State University, 2015. Print.
"Polarization." thePhysicsClassroom. The Physics Classroom, 2015. Web. 5 Dec. 2015.