SATHEE: Electrostatics Question 662

Electrostatics Question 662

Question: A uniformly charged and infinitely long line having a liner charge density $λ$ is placed at a normal distance $y$ from a point O. Consider a sphere of radius $R$ with O as the center and $R$ > $y$ . Electric flux through the surface of the sphere is

Options:

A) Zero

B) $\frac{2 λ R}{ε_{0}}$

C) $\frac{2 λ \sqrt{R^{2} - y^{2}}}{ε_{0}}$

D) $\frac{λ \sqrt{R^{2} + y^{2}}}{ε_{0}}$

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Answer:

Correct Answer: C

Solution:

[c] Electric flux $\oint_{s} \vec{E} . \vec{d} s = \frac{q_{i n}}{ε_{0}}$

$q_{i n}$ is the charge enclosed by the Gaussian Surface, which, in the present case, is the surface of the given sphere, As shown, length AB of line lies inside the sphere, in

$Δ O O^{'} A$ , $R^{2} = Y^{2} + {(O^{'} A)}^{2}$

$∴ O^{'} A = \sqrt{R^{2} - y^{2}}$ and $A B = 2 \sqrt{R^{2} - y^{2}}$

Charge on length AB is $2 \sqrt{R^{2} - y^{2}} \times λ$

Therefore, electric flux is $\oint_{S} \vec{E} . \vec{d} s = \frac{2 λ \sqrt{R^{2} - y^{2}}}{ε_{0}}$

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Electrostatics Question 662

Question: A uniformly charged and infinitely long line having a liner charge density $λ$ is placed at a normal distance $y$ from a point O. Consider a sphere of radius $R$ with O as the center and $R$ > $y$ . Electric flux through the surface of the sphere is

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 662

Question: A uniformly charged and infinitely long line having a liner charge density λ is placed at a normal distance y from a point O. Consider a sphere of radius R with O as the center and R > y . Electric flux through the surface of the sphere is

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: A uniformly charged and infinitely long line having a liner charge density $λ$ is placed at a normal distance $y$ from a point O. Consider a sphere of radius $R$ with O as the center and $R$ > $y$ . Electric flux through the surface of the sphere is