Charged Ring

This article will describe the Electric Field created by a uniformly charged thin ring and how to calculate the value of this field.

The Main Idea

Objects that create electric fields come in various shapes, including circular rings. Rings are

A Mathematical Model

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

This VPython code is a representation of adding up the electric fields created by individual pieces of a ring to figure out its electric field.

Step-by-Step Example

Below are examples of calculating the value and direction of the Electric Field caused by a ring positioned in the xy-plane with a radius [math]\displaystyle{ R }[/math] and total charge [math]\displaystyle{ q }[/math]. Physics 2212 only requires mastery of the simplest case -- the field at a location along the line that goes through the center of the ring, perpendicular to the plane that the circle is in. We'll call that line the [math]\displaystyle{ z-axis }[/math].

Connectedness

Calculating the electric field of a charged ring may seem like another exercise to practice visualizing the way a collection of charge can create a field and influence other objects around it, but it becomes very important in the study of Simple Circuits.

Electric fields created by rings of charge are the source of currents in circuits, which makes these little charged rings one of the most important components of daily life for almost all Americans and 83% of the citizens of the world. Rings of charge compounded into hollow wires of charge are a central part of past, present, and future human innovation.

History

Put this idea in historical context. Give the reader the Who, What, When, Where, and Why.

See also

Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?

Further reading

Books, Articles or other print media on this topic

External links

Here are some resources for further reading if you're interested:

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References

"Electric Field on the Axis of a Ring of Charge". University of Delaware Physics Library. Adapted from Stephen Kevan's lecture on Electric Fields and Charge Distribution. April 8, 1996. http://www.physics.udel.edu/~watson/phys208/exercises/kevan/efield1.html

Chabay, R., & Sherwood, B. (2015). Matter and Interactions (4th ed., Vol. 2, pp. 597-599). Wiley.

Energy Access Database. (n.d.). Retrieved December 6, 2015, from http://www.worldenergyoutlook.org/resources/energydevelopment/energyaccessdatabase/

Work in progress! - afrancis38