An infinitely long thin non-conduction wire is parallel to the z-axis and carries a uniform line charge density `lambda`. It pierces a thin non-conducting spherical shell of radius r in such a way that that the are PQ subtends an angle `120^(@)` at the centre O of the spherical shell, as shown in the figure. The permittivity of free space is `epsi_(0)`. which of the following statements is (are) true ?

Options

A. The electric flux through the shell is `sqrt3 R lambda//epsilon_0`
B. The Z-component of the electric field is zero at all the points on the surface of the shell
C. The electric flux through the shell is `sqrt2R lambda//epsilon_0`
D. The electric field is normal to the surface of the shell at all points.

Answer

A, B

Explanation

`Q_"enc"=lambdasqrt3R`
`phi-Q_"enc"/epsilon_0 =(sqrt3lambdaR)/epsilon_0`
Infinitely long line charge is parallel to Z-axis, hence its electric field being radially outwards becomes perpendicular to Z-axis everywhere.