Two large conducting plates having surface charge densities + σ and − σ respectively, are fixed 'd' distance apart. A small test charge q of mass m is attached to two identical springs as sh

Question

Two large conducting plates having surface charge densities + σ and − σ respectively, are fixed 'd' distance apart. A small test charge q of mass m is attached to two identical springs as shown in the adjacent figure. The charge q is now released from rest with springs in natural length. Then q will :- [neglect gravity]

TestHub · Accepted Answer

Field between plates: E = σ / ε 0 ​ ; equilibrium: 2 k x = qE . Extra displacement y : 2 k ( x + y ) − qE = ma ⇒ 2 k y = ma , so SHM with ω = 2 k / m ​ . (A) correct, (C) wrong. Energy: 2 1 ​ m v m a x 2 ​ = qE x − 2 1 ​ k x 2 ⇒ v m a x ​ = qE / 2 km ​ . Amplitude A = v m a x ​ / ω = qE /2 k = σ q /2 k ε 0 ​ . (B) correct, (D) wrong.

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