Question 669: Electrostatics & Capacitance

Question

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 ____________ $$	imes$$ 10
5
rad/s if q
2
= 10 C
2
.

Accepted Answer

Net force on free charged particle
$$F = {{k{q^2}} \over {{{(d + x)}^2}}} - {{k{q^2}} \over {{{(d - x)}^2}}}$$
$$F =  - k{q^2}\left[ {{{4dx} \over {{{({d^2} - {x^2})}^2}}}} ight]$$
$$a =  - {{4k{q^2}d} \over m}\left( {{x \over {{d^4}}}} ight)$$
$$a =  - \left( {{{4k{q^2}} \over {m{d^3}}}} ight)x$$
So, angular frequency
$$\omega  = \sqrt {{{4k{q^2}} \over {m{d^3}}}} $$
$$\omega  = \sqrt {{{4 	imes 9 	imes {{10}^9} 	imes 10} \over {1 	imes {{10}^{ - 6}} 	imes {1^3}}}} $$
$$\omega  = 6 	imes {10^8}$$ rad/sec
$$\omega  = 6000 	imes {10^5}$$ rad/sec

Electrostatics & Capacitance

Integer / Numeric Answer Type