Q 12-01-025JEE MainJEE Main 2026 (4 Apr, Shift 2)Hard
A rigid dipole undergoes a simple harmonic motion about its centre in the presence of an electric field $\vec{E}_1 = E_0\hat{x}$. If another electric field $\vec{E}_2 = 2E_0(\hat{y} + \hat{z})$ is introduced to the system, what will be the percentage change in the frequency of the oscillation (approximate)?
Answer: (A) $73\%$
Concept. A dipole's small oscillation has $\omega=\sqrt{pE/I}$, so frequency $\propto\sqrt{|\vec E|}$. Adding a second field changes the magnitude of the total field.
Step 1. New field. $\vec E=E_0\hat x+2E_0\hat y+2E_0\hat z$, $|\vec E|=E_0\sqrt{1+4+4}=3E_0$.
Step 2. Frequency ratio. $\sqrt3=1.732$: an increase of about $73\%$.
Answer. Option A.
Solution by Sreeraj P, M.Sc Physics
