JEE Main 2026 — Apr 4, Shift 2 — Physics solution

JEE Main2026Apr 4, Shift 2Physics

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)?

A
73%
B
63%
C
83%
D
53%

Solution

For a dipole in field $E$ , the small-oscillation frequency is $f = \frac{1}{2 π} \frac{P E}{I}$ , so $f \propto E$ .

Initial: $E_{i} = E_{0}$ .

Final: total field is $E = E_{0} \overset{x}{^} + 2 E_{0} \overset{y}{^} + 2 E_{0} \overset{z}{^}$ , with magnitude $∣ E ∣ = E_{0} 1 + 4 + 4 = 3 E_{0}$ .

$\frac{f _{2}}{f _{1}} = \frac{3 E _{0}}{E _{0}} = 3$ .

Percentage change $= (3 - 1) \times 100 \approx 0.732 \times 100 \approx 73%$ .

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