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A body of mass M and charge q is connected to a spring of spring constant k. It is oscillating along x-direction about its equilibrium position, taken to be at x = 0, with an amplitude A. An electric field E is applied along the x-direction. Which of the following statements is correct? [JEE-Main On line-2018]

1. The total energy of the system is 1/2 mω^2A^2 + 1/2 q^2E^2/k
2. The new equilibrium position is at a distance 2qE/k from x = 0
3. The new equilibrium position is at a distance qE/2k from x = 0
4. The total energy of the system is 1/2 mω^2A^2 − 1/2 q^2E^2/k

Correct answer: The total energy of the system is 1/2 mω^2A^2 + 1/2 q^2E^2/k

Solution

The correct option states that the total energy of the system is the sum of the potential energy stored in the spring and the potential energy due to the electric field. This reflects the conservation of energy principle, where both types of energy contribute to the overall energy of the oscillating charged mass in the presence of an electric field.

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