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  4. Two large insulating plates having surface charge densities + σ and -σ are fixed at a distance d from each other. A small test charge q of mass m is attached to two identical springs as shown in the figure. The charge q is now released from rest with springs in natural length. Then q will (neglect gravity) <img class=img-fluid question-image alt=Question src=https://cdn.tardigrade.in/q/nta/p-9yn1qfon0wzr.png />

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Q. Two large insulating plates having surface charge densities $+ \, \sigma $ and $-\sigma $ are fixed at a distance $d$ from each other. A small test charge $q$ of mass $m$ is attached to two identical springs as shown in the figure. The charge $q$ is now released from rest with springs in natural length. Then $q$ will (neglect gravity)



Question

NTA AbhyasNTA Abhyas 2020Electrostatic Potential and Capacitance

Solution:

Electric field between plates is uniform hence electrostatic force due to this field is constant. Angular frequency does not change by constant force equilibrium position will be at the point where $2kx_{0}=q\times \frac{\sigma }{\in _{0}};x_{0}=\frac{\sigma q}{2 k \in _{0}}$
$x_{0}$ is also the amplitude of oscillation