A rigid dipole undergoes a simple harmonic motion about its centre in the presence of an electric field $\overrightarrow{\mathrm{E}}_{1}=\mathrm{E}_{0} \hat{\mathrm{x}}$. If another electric field $\overrightarrow{\mathrm{E}}_{2}=2 \mathrm{E}_{0}(\hat{\mathrm{y}}+\hat{\mathrm{z}})$ is introduced to the system, what will be the percentage change in the frequency of the oscillation (approximate) ?

JEE Main · 2026 · 04 Apr 2026 · Shift 2 · Elasticity & SHM

A rigid dipole undergoes a simple harmonic motion about its centre in the presence of an electric field

E_{1} = E_{0} \overset{x}{^}

. If another electric field

E_{2} = 2 E_{0} (\overset{y}{^} + \overset{z}{^})

is introduced to the system, what will be the percentage change in the frequency of the oscillation (approximate) ?

Answer: (A)

For a dipole oscillating in a uniform field the frequency is

f = \frac{1}{2 π} \frac{pE}{I}

, so

f \propto E

. With

E_{1}

alone the field magnitude is

E_{0}

. Adding

E_{2} = 2 E_{0} (\overset{y}{^} + \overset{z}{^})

gives a net field

E_{0} \overset{x}{^} + 2 E_{0} \overset{y}{^} + 2 E_{0} \overset{z}{^}

of magnitude

E_{0} 1 + 4 + 4 = 3 E_{0}

. The frequency therefore changes by the factor

3 E_{0} / E_{0} = 3

, a fractional change of

3 - 1 \approx 0.73

. The frequency increases by about

73%

JEE Main · 2026 · 04 Apr 2026 · Shift 2 · Single correct option