SATHEE: Electrostatics Question 265

Electrostatics Question 265

Question: nnCapacitance of a capacitor made by a thin metal foil is $2 μ F$ . If the foil is folded with paper of thickness $0.15 m m$ , dielectric constant of paper is 2.5 and width of paper is $400 m m$ , then length of foil will be [RPET 1997]

Options:

A) $- \frac{Q}{4} (1 + 2 \sqrt{2})$

B) $\frac{Q}{4} (1 + 2 \sqrt{2})$

C) $- \frac{Q}{2} (1 + 2 \sqrt{2})$

D) $\frac{Q}{2} (1 + 2 \sqrt{2})$

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Answer:

Correct Answer: B

Solution:

If all charges are in equilibrium, system is also in equilibrium.

Charge at centre: charge q is in equilibrium because no net force acting on it corner charge:

If we consider the charge at corner B. This charge will experience following forces $F_{A} = k \frac{Q^{2}}{a^{2}},$

$F_{C} = \frac{k Q^{2}}{a^{2}}$ , $F_{D} = \frac{k Q^{2}}{{(a \sqrt{2})}^{2}} and F_{O} = \frac{K Q q}{{(a \sqrt{2})}^{2}}$

Force at B away from the centre = $F_{A C} + F_{D}$

$= \sqrt{F_{A}^{2} + F_{C}^{2}} + F_{D} = \sqrt{2} \frac{k Q^{2}}{a^{2}} + \frac{k Q^{2}}{2 a^{2}} = \frac{k Q^{2}}{a^{2}} (\sqrt{2} + \frac{1}{2})$

Force at B towards the centre $= F_{O} = \frac{2 k Q q}{a^{2}}$

For equilibrium of charge at B, $F_{A C} + F_{D} = F_{O}$

therefore $\frac{K Q^{2}}{a^{2}} (\sqrt{2} + \frac{1}{2}) = \frac{2 K Q q}{a^{2}}$

therefore $q = \frac{Q}{4} (1 + 2 \sqrt{2})$

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Electrostatics Question 265

Question: nnCapacitance of a capacitor made by a thin metal foil is $2 μ F$ . If the foil is folded with paper of thickness $0.15 m m$ , dielectric constant of paper is 2.5 and width of paper is $400 m m$ , then length of foil will be [RPET 1997]

Options:

Answer:

Solution:

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चिकित्सा तैयारी

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Electrostatics Question 265

Question: nnCapacitance of a capacitor made by a thin metal foil is 2μF . If the foil is folded with paper of thickness0.15mm , dielectric constant of paper is 2.5 and width of paper is400mm , then length of foil will be [RPET 1997]

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

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Question: nnCapacitance of a capacitor made by a thin metal foil is $2 μ F$ . If the foil is folded with paper of thickness $0.15 m m$ , dielectric constant of paper is 2.5 and width of paper is $400 m m$ , then length of foil will be [RPET 1997]