SATHEE: Electrostatics Question 251

Electrostatics Question 251

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 [MP PET 2003]

Options:

A) $x = \frac{d}{\sqrt{2}}$

B) $x = \frac{d}{2}$

C) $x = \frac{d}{2 \sqrt{2}}$

D) $x = \frac{d}{2 \sqrt{3}}$

Show Answer

Answer:

Correct Answer: C

Solution:

Suppose third charge is similar to Q and it is q So net force on it

$F_{n e t} = 2 F cos θ$ Where $F = \frac{1}{4 π ε_{0}} . \frac{Q q}{(x^{2} + \frac{d^{2}}{4})}$ and $\cos θ = \frac{x}{\sqrt{x^{2} + \frac{d^{2}}{4}}}$

$F_{n e t} = 2 \times \frac{1}{4 π ε_{0}} . \frac{Q q}{(x^{2} + \frac{d^{2}}{4})} \times \frac{x}{{(x^{2} + \frac{d^{2}}{4})}^{1 / 2}}$

$= \frac{2 Q q x}{4 π ε_{0} {(x^{2} + \frac{d^{2}}{4})}^{3 / 2}}$

For $F_{n e t}$ to be maximum $\frac{d F_{n e t}}{d x} = 0$

i.e. $\frac{d}{d x} [\frac{2 Q q x}{4 π ε_{0} {(x^{2} + \frac{d^{2}}{4})}^{3 / 2}}] = 0$

or $[{(x^{2} + \frac{d^{2}}{4})}^{- 3 / 2} - 3 x^{2} {(x^{2} + \frac{d^{2}}{4})}^{- 5 / 2}] = 0$ i.e. $x = \pm \frac{d}{2 \sqrt{2}}$

पिछला

अगला

Electrostatics Question 251

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 [MP PET 2003]

Options:

Answer:

Solution:

इंजीनियरिंग की तैयारी

चिकित्सा तैयारी

एनसीईआरटी पुस्तकें और समाधान

महत्वपूर्ण संसाधन

अन्य संसाधन

पाठ्यक्रम

परीक्षा मंच

नमूना मॉक टेस्ट

सदस्यता

एनसीईआरटी व्यायाम वीडियो समाधान

Electrostatics Question 251

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 [MP PET 2003]

Options:

Answer:

Solution:

इंजीनियरिंग की तैयारी

चिकित्सा तैयारी

एनसीईआरटी पुस्तकें और समाधान

महत्वपूर्ण संसाधन

अन्य संसाधन

पाठ्यक्रम

परीक्षा मंच

नमूना मॉक टेस्ट

सदस्यता

एनसीईआरटी व्यायाम वीडियो समाधान

Menu