A particle of mass 1 mg and charge q is lying at the mid-point of two stationary particles kept a distance 2 m apart, each carrying the same charge q. If the free charged particle is displaced from its equilibrium position through a distance x (x1 m), the particle executes SHM. Its angular frequenc…

Question

A particle of mass 1 mg and charge q is lying at the mid-point of two stationary particles kept a distance 2 m apart, each carrying the same charge q. If the free charged particle is displaced from its equilibrium position through a distance x (x1 m), the particle executes SHM. Its angular frequency of oscillation will be ×10⁵ rad s⁻¹ if q²=10 C².

Accepted Answer

6000. Each fixed charge sits at a=1 m from the mid-point. Displace the free charge by x along the line: F=kq²[1/((a-x)²)-1/((a+x)²)]≈(4kq²)/(a³)x, directed back to the centre. ω²=(4kq²)/(ma³)=(4×9×10⁹×10)/(10⁻⁶×1)=3.6×10¹⁷. ω=6×10⁸ rad s⁻¹=6000×10⁵ rad s⁻¹.

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