A particle of mass 1 mg and charge q is lying at the mid-point of two stationary particles kept at a distance 2 m when each is carrying same charge q'. If the free charged particle is displaced from its equilibrium position through distance 'x' (x << 1m). The particle executes SHM. Its angular frequency of oscillation will be ______ × 10? rad/s if q' = 1 C.

F_net = -kq²/ (l+x)² + kq²/ (l-x)²
= kq² [ (l+x)² - (l-x)² / (l²-x²)² ]
= kq² [ 4lx / (l²-x²)² ]
For x << l,
ma ≈ -4kq²x / l³
a = - (4kq²/ml³)x
ω² = 4kq²/ml³
ω = √ (4kq²/ml³)
= √ (4 × 9×10? × 10 / (1×10? × 1)
= 6 × 10? rad/s
= 6000 × 10? rad/s

 

<p>F_net = -kq²/ (l+x)² + kq²/ (l-x)²<br>= kq² [ (l+x)² - (l-x)² / (l²-x²)² ]<br>= kq² [ 4lx / (l²-x²)² ]<br>For x &lt;&lt; l, <br>ma ≈ -4kq²x / l³<br>a = - (4kq²/ml³)x<br>ω² = 4kq²/ml³<br>ω = √ (4kq²/ml³)<br>= √ (4 × 9×10? × 10 / (1×10? × 1)<br>= 6 × 10? rad/s<br>= 6000 × 10? rad/s</p><div><div><picture><source srcset="" media=" (max-width: 500px)"><img src="https://images.shiksha.com/mediadata/images/1755600063phprbttdP.jpeg" alt="" width="211" height="56" loading="lazy"></picture></div></div><p>&nbsp;</p>

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