Oscillating electron

Consider a uniformly positively charged non conducting sphere of volume charge density $$\rho$$. An electron is released from its surface.

Considering that the amplitude of the oscillations is less than the sphere's radius, find the time period of its periodic motion (in microseconds).

$$\textbf{Details and Assumptions}$$

• $$\rho = 2 \times 10^{-7} \ \text{C}/ \text{m}^3$$
• $$m_e=9.1 \times 10^{-31} \ \text{kg}$$
• $$\epsilon_0=8.85 \times 10^{-12} \ \text{F}/\text{m}$$
• $$e$$ (charge on electron)$$=-1.6 \times 10^{-19} \ \text{C}$$
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