Electromagnetism - Oscillation

Question 3-4: refer to a thin, nonconducting ring of radius R, as shown below, which has a charge Q uniformly spread out on it.


A small particle of mass m and charge –q is placed at point P and released. If R ≫ x, the particle will undergo oscillations along the axis of symmetry with an angular frequency that is equal to:



(GR9677 #04)

Solution:

Felectric = kqQ/r²
Fcentripetal = mv²/r = mω²r

FFc
kqQ/r² = mω²r
ω² = kqQ/mr³

with
= 1/4πɛ0
r²  = R² + x²
R ≫ x
r² ∼ R²  → r³ ∼ R³

ω = √(qQ/4πɛ0mR3)

Answer: A

Notes:
see problem GR9277 #65

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