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Question

Assuming mass m of the charged particle, find time period of oscillation
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  1. 2πq1q4πε0a3m
  2. 2π4πε0a3mq1q
  3. π2πq1q4πε0q3m
  4. none of these

A
π2πq1q4πε0q3m
B
none of these
C
2πq1q4πε0a3m
D
2π4πε0a3mq1q
Solution
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E0=2E1cosθ=q4πε0(x2+a2)xx2+a2
q1E=F=mf=q1qx4πε0(x2+a2)3/2 as x << a, neglecting
x2 as compared to acceleration, f=q1q2x4πε0a3m
Comparing it with f=ω2x
ωq1q4πε0a3m or T=2π4πε0a3mq1q

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