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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 the 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?

Asked in JEE Main Online 2018 · Deflection and projectile motion

• (1) The total energy of the system is 1/2mω²A²-1/2(q²E²)/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 1/2mω²A²+1/2(q²E²)/k.

Step-by-step solution

Why the other options are wrong

• (2) Doubles the shift; balancing kx₀=qE gives x₀=(qE)/k, with no factor of 2.
• (3) Halves the shift, as if the spring force at the new equilibrium were 2kx₀.
• (4) Gets the magnitude right but the sign wrong: the constant force lowers the energy measured about the old origin by 1/2(q²E²)/k, it does not raise it.

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