H.Tahsiri

Dropping an electron into a ring of charge.

```Learning Goals:Electric Potential. Electric Field. F = ma & equation of motion.
Position. Velocity. Acceleration.Taylor Series Expansion. The Gradient."Mathematica" solutions.```

Figure shows a thin ring of radius R with a total uniform positive charge q around its circumference. We may imagine the ring to be made of plastic or some other insulator, so that the charges can be regarded a fixed " Static" in place. An electron is released along the axis of the ring. We ask the following questions relevant to students course work.

Q1. Explain the conceptual physical outcome of this problem (Click on Answer Q1)

Q2. How can I find the electrostatic potential at a point p on the axes of the ring? (Click on Answer to Q2)

Q3. Can I approximate the potential and the electric field at a point p near the center ? (Yes, use Taylor Series Expansion and the Gradient of the potential). (Click on Answer to Q3)

Q4. If I drop an electron near the center at p ; can I use F = ma to solve for the motion of the electron ? ( Click on Answer to Q4)

Q5. Explain your physical results . Was your intuitive guess correct ? ( Click on Answer to Q5 )

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