Systems of Charged Objects

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In many cases in the real world, there are more than one charge contributing to an interaction. However, in some simple cases, one can choose a system (and ignore external forces) by choosing a system of charges and observing the changes of Kinetic energy (K_sys) and Potential energy (U).

The Main Idea

In physics, a physical system is a region of the physical universe to be analyzed, and everything outside the system is known as the "surroundings." The same logic can be applied to a system of charges; only energy changes within the system need to be analyzed.

A Mathematical Model

ΔK_sys + ΔU = 0 (zero work done by surroundings)

A Computational Model

How do we visualize or predict using this topic. Consider embedding some vpython code here Teach hands-on with GlowScript

Example

Consider a system of two uniformly charged plates of a capacitor and a single proton. In the region between the plates, there is nearly uniform electric field and external forces can be ignored. The proton is traveling through the right between the plates.

While the proton is between the plates, an electric force is acting on it. The direction of the force is to the right (Electric field points to the right: away from the positive plate and toward the negative plate) F_electric = Q_proton * E

Question: Will the Kinetic Energy (K) of the proton increase or decrease as a result of this force?

Answer: Because the force is in the same direction as the motion of the particle (the displacement, Δx), the Kinetic Energy will increase.

ΔK_proton + ΔU_electric = 0

The change in electric potential energy is equal to the negative of internal work of the system.

ΔU_electric = -(W_intenal) = -(F_electric * Δx) ΔU_electric = -(Q_proton * E * Δx)

Because E and Δx are in the same direction, their product is positive.

ΔK_proton + ΔU_electric = 0 ΔK_proton = -(ΔU_electric) ΔK_proton = Q_proton * E * Δx , which is a positive value

Kinetic energy of the proton increases because ΔK_proton is positive.

Connectedness

1. How is this topic connected to something that you are interested in?
2. How is it connected to your major?
3. Is there an interesting industrial application?

History

Leibniz first defined the concept of "energy" as a "vis viva" or living force. He stated that it was mass times its velocity squared.

In 1829, Coriolis modernized the notion of "kinetic energy" as we know it today. In 1853, Rankine developed the idea of "potential energy" of a system.

Using energy as a method of relating masses, displacement, velocity, and other vector quantities as scalars simplifies calculations. Thinking of physical interactions as changes of energy within a system (and also the external forces as 'work' on a system) revolutionized the way many problems were approached and solved.

See also

Further reading

Eugene Hecht, “An Historico-Critical Account of Potential Energy: Is PE Really Real?” The Physics Teacher 41 (Nov 2003): 486-93.

Katalin Martinás, “Aristotelian Thermodynamics,” Thermodynamics: history and philosophy: facts, trends, debates (Veszprém, Hungary 23-28 July 1990), 285-303.

References

Chabay, Ruth and Bruce Sherwood. Matter and Interactions Volume II: Electric and Magnetic Interactions. 4th ed. Danvers, MA: John Wiley and Sons, Inc., 2015. Print.