An infinitely long thin non-conducting wire is parallel to the z - axis and carries a uniform line charge…

1. The electric flux through the shell is $\sqrt{3}R\lambda /{ϵ}_0$
2. The z - component of the electric field is zero at all the points on the surface of the shell
3. The electric flux through the shell is $\sqrt{2}R\lambda /{ϵ}_0$
4. The electric field is normal to the surface of the shell at all points

Solution

Field due to straight wire is perpendicular to the wire and radially outward. Hence $E_z = 0$
Length, $PQ=2R\sin 60=\sqrt{3}R$ According to Gauss's law
Total flux $=\oint \overrightarrow{E}.\overrightarrow{ds}=\frac{q_{in}}{{\in }_0}=\frac{\lambda \sqrt{3}R}{{\in }_0}$

Asked in: JEE Advanced 2018 (Paper 2)

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