An infinitely long thin non-conducting wire is parallel to the z - axis and carries a uniform line charge density λ . It pierces a thin non-conducting spherical shell of radius R in such a way that th

Question

An infinitely long thin non-conducting wire is parallel to the z - axis and carries a uniform line charge density $λ$ . It pierces a thin non-conducting spherical shell of radius $R$ in such a way that the arc $P Q$ subtends an angle $120^{o}$ at the centre $O$ of the spherical shell, as shown in the figure. The permittivity of free space is $ϵ_{0}$ . Which of the following statements is (are) true?

TestHub · Accepted Answer

Field due to straight wire is perpendicular to the wire and radially outward. Hence $E_{z} = 0$
Length, $P Q = 2 R \sin 60 = \sqrt{3} R$ According to Gauss's law
Total flux $= \oint \vec{E} . \vec{d s} = \frac{q_{i n}}{\in_{0}} = \frac{λ \sqrt{3} R}{\in_{0}}$

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