A particle of mass 1 mg and charge q is lying at the mid-point of two… | JEE Main 2021 (25 Jul, Shift 1)

Q30JEE Main 2021 · 25 JUL · SHIFT 1Medium

Motion of Charges in an Electric Field

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 << 1 m), the particle executes SHM. Its angular frequency of oscillation will be ____________ $\times$ 105 rad/s if q2 = 10 C2.

Numerical answer type. Work it out, then open the answer.

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Answer: 6000

Fixed charges at distance $a = 1\text{ m}$ on each side; displacement $x$ along the line gives $F \approx -\frac{4kq^2}{a^3}x$ .
$\omega = \sqrt{\frac{4kq^2}{ma^3}} = \sqrt{\frac{4 \times 9 \times 10^{9} \times 10}{10^{-6} \times 1}} = \sqrt{3.6 \times 10^{17}}$
$\omega = 6 \times 10^{8} = 6000 \times 10^{5}\text{ rad/s}$
So the answer is 6000.

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Motion of Charges in an Electric Field question from JEE Main 2021 (25 Jul, Shift 1)

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