SATHEE: Electrostatics Question 670

Electrostatics Question 670

Question: An electric dipole is situated in an electric field of uniform intensity $E$ whose dipole moment is p and moment of inertia is I. If the dipole is displaced slightly from the equilibrium position, then the angular frequency of its oscillations is

Options:

A) ${(\frac{p E}{l})}^{1 / 2}$

B) ${(\frac{p E}{l})}^{3 / 2}$

C) ${(\frac{l}{p E})}^{1 / 2}$

D) ${(\frac{p}{l E})}^{1 / 2}$

Show Answer

Answer:

Correct Answer: A

Solution:

[a] When dipole is given a small angular displacement $θ$ about its equilibrium position, the restoring torque will be $τ = - p E \sin θ = - p E θ (a s s i n θ = θ)$

or $I \frac{d^{2} θ}{d t^{2}} = - p E θ (a s τ = I α = I \frac{d^{2} θ}{d t^{2}})$

or $\frac{d^{2} θ}{d t^{2}} = - ω^{2} θ with ω^{2} = \frac{p E}{I} \Rightarrow ω = \sqrt{\frac{p E}{I}}$

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Electrostatics Question 670

Question: An electric dipole is situated in an electric field of uniform intensity E whose dipole moment is p and moment of inertia is I. If the dipole is displaced slightly from the equilibrium position, then the angular frequency of its oscillations is

Options:

Answer:

Solution:

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Question: An electric dipole is situated in an electric field of uniform intensity $E$ whose dipole moment is p and moment of inertia is I. If the dipole is displaced slightly from the equilibrium position, then the angular frequency of its oscillations is