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24.6: Calculations of Electric Potential I

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Calculations of Electric Potential I

24.6: Calculations of Electric Potential I

Consider a ring of radius R with a uniform charge density λ. What will the electric potential be at point M, which is located on the axis of the ring at a distance x from the center of the ring?

The ring is divided into infinitesimal small arcs such that point M is equidistant from all the arcs. Here, the cylindrical coordinate system is used to calculate the electric potential at point M. A general element of the arc between angles θ and θ + dθ is of the length Rdθ and has a charge of λRdθ.


The distance between this element of the ring and the point M is


The potential at point M due to the charge on the whole ring is


Integrating the above equation over the limits gives,


Here, 2πRλ accounts for the whole charge on the ring; therefore, the above equation can be written as


This result is expected because point M is equidistant from all the infinitesimal ring elements, and the total potential will be similar to if the total charge were positioned at a common distance from point M.

Suggested Reading


Calculations Electric Potential Ring Radius Charge Density Point M Axis Distance X Center Infinitesimal Small Arcs Cylindrical Coordinate System General Element Angles Length Rd Charge Distance Between Element And Point M Potential At Point M Integration Limits 2πRσ Common Distance

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