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)

Q**3.** 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 )

- Answer to Question 1 (Conceptual outcome)
- Answer to Question 2 (Electric potential )
- Answer to Question 3 (Potential and field near the center)
- Answer to Question 4 (Electron's equation of motion)
- Answer to Question 5 (Explain physical results)

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**Expand
your Knowledge** ( Taylor series, gradient and ** Mathematica **Solutions
)