Question

Review. A negatively charged particle $-q$ is placed at the center of a uniformly charged ring, where the ring has a total positive charge $Q$ as shown in Figure P23.74. The particle, confined to move along the $x$ axis, is moved a small distance $x$ along the axis (where $x<<a$ ) and released. Show that the particle oscillates in simple harmonic motion with a frequency given by $$f=\frac{1}{2 \pi}\left(\frac{k_{.} q Q}{m a^{3}}\right)^{1 / 2}$$

          Review. A negatively charged particle $-q$ is placed at the center of a uniformly charged ring, where the ring has a total positive charge $Q$ as shown in Figure P23.74. The particle, confined to move along the $x$ axis, is moved a small distance $x$ along the axis (where $x<<a$ ) and released. Show that the particle oscillates in simple harmonic motion with a frequency given by $$f=\frac{1}{2 \pi}\left(\frac{k_{.} q Q}{m a^{3}}\right)^{1 / 2}$$

Added by Milagros M.

University Physics with Modern Physics

Hugh D. Young 14th Edition

Instant Answer

Solved by Expert Vishal Gupta

01/09/2022

Step 1

Step 1:** The electric field at point B on the axis of the ring is given by: \[ E = \frac{k \cdot Q \cdot x}{a^2 + x^2} \] ** Show more…

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Review. A negatively charged particle $-q$ is placed at the center of a uniformly charged ring, where the ring has a total positive charge $Q$ as shown in Figure P23.74. The particle, confined to move along the $x$ axis, is moved a small distance $x$ along the axis (where $x<<a$ ) and released. Show that the particle oscillates in simple harmonic motion with a frequency given by $$f=\frac{1}{2 \pi}\left(\frac{k_{.} q Q}{m a^{3}}\right)^{1 / 2}$$