Polarization of a conductor: Difference between revisions
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'''Ionic Solutions''' | '''Ionic Solutions''' | ||
Ionic solutions, such as KCl or NaCl or NaI (solutions in which the ions dissociate), have individual ions of the dissociated particles. For example, a solution of NaI will have Na+, I-, and because it is an aqueous solution, some H+ and OH- as well. When an electric field is applied to this solution, the particles (as you'd imagine) move in the direction of the force applied by the electric field. However, the interesting concept here is that the charged particles move in a direction and accumulate, therefore creating a charge gradient, '''which in turn creates its own electric field!''' This can be shown in Figure 1, taken from the textbook. While ions are constantly moving, this is an accurate snapshot of what would be expected in the event of applied field/force. Furthermore, while ions move around the solution at all times (it is a conductor after all), there is a measurable excess of ions on the edges that generates the field. | Ionic solutions, such as KCl or NaCl or NaI (solutions in which the ions dissociate), have individual ions of the dissociated particles. For example, a solution of NaI will have Na+, I-, and because it is an aqueous solution, some H+ and OH- as well. When an electric field is applied to this solution, the particles (as you'd imagine) move in the direction of the force applied by the electric field. However, the interesting concept here is that the charged particles move in a direction and accumulate, therefore creating a charge gradient, '''which in turn creates its own electric field!''' This can be shown in Figure 1, taken from the textbook. While ions are constantly moving, this is an accurate snapshot of what would be expected in the event of applied field/force. Furthermore, while ions move around the solution at all times (it is a conductor after all), there is a measurable excess of ions on the edges that generates the field. | ||
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'''The net electric field is the superposition of the applied field and the field generated by the charge gradient and excess ion concentrations on the edges.''' | '''The net electric field is the superposition of the applied field and the field generated by the charge gradient and excess ion concentrations on the edges.''' | ||
===A Mathematical Model=== | |||
= | In the phenomenon described above, when the external field is applied on an ionic solution, the Na+ and I- ions will move and bounce around a good bit, but due to collisions, they do not maintain a specific speed or trajectory. This is in spite of whether or not the force experienced is constant. In order to keep the ions moving at constant speed, also known as the drift speed, a constant electric field must be applied. This is modeled mathematically using the following equation: | ||
'''v = u*Enet''' | |||
where v is the drift speed, u is the mobility of the charge ((m/s)/(N/C)), and Enet is the net electric field applied to the ionic solution. | |||
What are the mathematical equations that allow us to model this topic. For example <math>{\frac{d\vec{p}}{dt}}_{system} = \vec{F}_{net}</math> where '''p''' is the momentum of the system and '''F''' is the net force from the surroundings. | What are the mathematical equations that allow us to model this topic. For example <math>{\frac{d\vec{p}}{dt}}_{system} = \vec{F}_{net}</math> where '''p''' is the momentum of the system and '''F''' is the net force from the surroundings. | ||
Revision as of 18:28, 17 April 2016
THIS HAS BEEN CLAIMED BY JAY SHAH Short Description of Topic
The Main Idea
Based on the definition of a conductor, it is easily assumed that stronger conductors can have charged particles moving more freely within it and in larger distances. There are two main situations where this can be observed. The first is in ionic solutions:
Ionic Solutions
Ionic solutions, such as KCl or NaCl or NaI (solutions in which the ions dissociate), have individual ions of the dissociated particles. For example, a solution of NaI will have Na+, I-, and because it is an aqueous solution, some H+ and OH- as well. When an electric field is applied to this solution, the particles (as you'd imagine) move in the direction of the force applied by the electric field. However, the interesting concept here is that the charged particles move in a direction and accumulate, therefore creating a charge gradient, which in turn creates its own electric field! This can be shown in Figure 1, taken from the textbook. While ions are constantly moving, this is an accurate snapshot of what would be expected in the event of applied field/force. Furthermore, while ions move around the solution at all times (it is a conductor after all), there is a measurable excess of ions on the edges that generates the field.
The net electric field is the superposition of the applied field and the field generated by the charge gradient and excess ion concentrations on the edges.
A Mathematical Model
In the phenomenon described above, when the external field is applied on an ionic solution, the Na+ and I- ions will move and bounce around a good bit, but due to collisions, they do not maintain a specific speed or trajectory. This is in spite of whether or not the force experienced is constant. In order to keep the ions moving at constant speed, also known as the drift speed, a constant electric field must be applied. This is modeled mathematically using the following equation:
v = u*Enet
where v is the drift speed, u is the mobility of the charge ((m/s)/(N/C)), and Enet is the net electric field applied to the ionic solution.
What are the mathematical equations that allow us to model this topic. For example [math]\displaystyle{ {\frac{d\vec{p}}{dt}}_{system} = \vec{F}_{net} }[/math] where p is the momentum of the system and F is the net force from the surroundings.
A Computational Model
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