SATHEE: Electrostatics 3 Question 18

Electrostatics 3 Question 18

18. An infinitely long uniform line charge distribution of charge per unit length $λ$ lies parallel to the $y$ -axis in the $y$ - $z$ plane at $z = \frac{\sqrt{3}}{2} a$ (see figure). If the magnitude of the flux of the electric field through the rectangular surface $A B C D$ lying in the $x - y$ plane with its centre at the origin is

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Answer:

Correct Answer: 18. (6)

Solution:

$A N B P$ is cross-section of a cylinder of length $L$ . The line charge passes through the centre $O$ and perpendicular to paper.

$\begin{matrix} A M = \frac{a}{2}, M O = \frac{\sqrt{3} a}{2} \\ ∴ ∠ A O M = \tan^{- 1} \frac{A M}{O M} \\ = \tan^{- 1} \frac{1}{\sqrt{3}} = 30^{\circ} \end{matrix}$

Electric flux passing from the whole cylinder

$φ = \frac{q_{in}}{ε_{0}} = \frac{λ L}{ε_{0}}$

$∴$ Electric flux passing through $A B C D$ plane surface (shown only $A B) =$ Electric flux passing through cylindrical surface $A N B$

$\begin{aligned} = \frac{60^{\circ}}{360^{\circ}} (φ) \\ = \frac{λ L}{6 ε_{0}} \\ ∴ n & = 6 \end{aligned}$

Electrostatics 3 Question 18

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Electrostatics 3 Question 18

Answer:

Solution:

Engineering Preparation

Medical Preparation

NCERT Books & Solutions

Important Resources

Other Resources

Syllabus

Test Platform

Sample Mock Test

Mentorship

NCERT Exercise Video Solution

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