Electric Field and Electric Potential: Difference between revisions
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If we think back to the study of conservation of energy, we know that the change in potential energy of a system is work, which is a force being applied over a distance. Since force and distance are vectors, integrating up over the distance of applied force, we obtain: | If we think back to the study of conservation of energy, we know that the change in potential energy of a system is work, which is a force being applied over a distance. Since force and distance are vectors, integrating up over the distance of applied force, we obtain: | ||
<math>{\ | <math>{\DeltaU=\int_i^f {\vec{F} • \vec{ds}}}</math>. By analogy, we define the electric potential as the energy per coulomb, or potential energy divided by charge: | ||
<math>{\ | <math>{\DeltaV=\int_i^f {\vec{E} • \vec{ds}}}</math>. | ||
Observe both sets of equations: the two for Electric Field and Electric Force, and the two for Electric Potential and Potential Energy. We see that they are all related mathematically. If we integrate the electric force, that is, sum the contributions of force over a finite distance, we obtain the change in potential energy. Dividing by the charge, we obtain the potential difference or electric potential, which we see is simply the integral of the electric field applied over a distance. | Observe both sets of equations: the two for Electric Field and Electric Force, and the two for Electric Potential and Potential Energy. We see that they are all related mathematically. If we integrate the electric force, that is, sum the contributions of force over a finite distance, we obtain the change in potential energy. Dividing by the charge, we obtain the potential difference or electric potential, which we see is simply the integral of the electric field applied over a distance. | ||
Revision as of 14:49, 25 November 2016
Claimed by Terrence Connors
The Main Idea
In physics, many phenomena that we observe are interrelated in some capacity. In the study of electricity and magnetism, several important physical quantities that play a crucial role in understanding physical interactions are derived from one another. Electric Field is a concept that is discussed early in most Electricity and Magnetism curricula, but it has enormous impact once we discover that it tells us information about Electric Potential, and from that, Potential Energy. This helps physicists to understand both the mechanics of a system, and the quantized nature of a system.
A Mathematical Model
We know that the electric force, given by Coulomb's Law, is [math]\displaystyle{ {\vec{F}=q\vec{E}} }[/math]. We also know that electric field and electric force are closely related, the electric field being equal to the electric force divided by the amount of charge [math]\displaystyle{ {\vec{E}=\frac{\vec{F}}{q}} }[/math].
If we think back to the study of conservation of energy, we know that the change in potential energy of a system is work, which is a force being applied over a distance. Since force and distance are vectors, integrating up over the distance of applied force, we obtain: [math]\displaystyle{ {\DeltaU=\int_i^f {\vec{F} • \vec{ds}}} }[/math]. By analogy, we define the electric potential as the energy per coulomb, or potential energy divided by charge: [math]\displaystyle{ {\DeltaV=\int_i^f {\vec{E} • \vec{ds}}} }[/math].
Observe both sets of equations: the two for Electric Field and Electric Force, and the two for Electric Potential and Potential Energy. We see that they are all related mathematically. If we integrate the electric force, that is, sum the contributions of force over a finite distance, we obtain the change in potential energy. Dividing by the charge, we obtain the potential difference or electric potential, which we see is simply the integral of the electric field applied over a distance.
A Computational Model
How do we visualize or predict using this topic. Consider embedding some vpython code here Teach hands-on with GlowScript
Examples
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Middling
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Connectedness
- How is this topic connected to something that you are interested in?
- How is it connected to your major?
- Is there an interesting industrial application?