One end of a spring of negligible unstretched length and spring constant k is fixed at the origin (0, 0). A point particle of mass m carrying a positive charge q is attached at its other end. The entire system is kept on a smooth horizontal surface. When a point dipole 𝐩 pointing towards the charge q is fixed at the origin, the spring gets stretched to a length λ and attains a new equilibrium position (see figure below). If the point mass is now displaced slightly by Δλ << λ from its equilibrium position and released, it is found to oscillate at frequency 1 δ k m \frac{1}{\delta}\sqrt{\frac{k}{m}} δ 1 ​ m k ​ ​ . The value of δ is.

Physics · Electrostatic

JEE Advanced 2020

One end of a spring of negligible unstretched length and spring constant k is fixed at the origin (0, 0). A point particle of mass m carrying a positive charge q is attached at its other end. The entire system is kept on a smooth horizontal surface. When a point dipole 𝐩 pointing towards the charge q is fixed at the origin, the spring gets stretched to a length λ and attains a new equilibrium position (see figure below). If the point mass is now displaced slightly by Δλ << λ from its equilibrium position and released, it is found to oscillate at frequency 1δkm\frac{1}{\delta}\sqrt{\frac{k}{m}} . The value of δ is.

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