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1. In lecture, we derived the electric field a height z above the center of a thin ring of charge with constant charge per unit length λ Lets assume here that λ > 0. Suppose a negative point charge-q with mass m is placed a very small distance above the center of the ring. Show that the point charge undergoes simple harmonic motion and find the frequency of small oscillations. Hint: show that near the center of the ring the force on the point charge resembles Hookes law.

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