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 `sqrt(3) R lambda // epsi_(0)`
B. The z -component of the electric field is zero at all the point on the surface of the shell
C. The electric flux thourgh the shell is `sqrt(2)R lambda // in_(0)`
D. The electric field is normal to the surface of the shell at all points

Answer

A, B

Explanation

Flux through shell is
`phi=(q_(enc))/(epsi_(0))=(lamda(2Rsin60^(@))/(in_(0))=(sqrt3lamdaR)/(in_(0))` (A is correct)
Field due to infinite charged wire is perpendicular to the wire
`thereforeE_(z)=0` at all points (B is correct)