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 PQ subtends an angle 120° at the centre O of the spherical shell, as shown in the figure. The permittivity of free space is ε0. Which of the following statements is (are) true?

(A) The electric flux through the shell is √3Rλ/ε0
(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 √2Rλ/ε0
(D) The electric field is normal to the surface of the shell at all points

Answer 1

Answer (A,B)

solution

Field due to straight wire is perpendicular to the wire & radially outward. Hence Ez = 0
Length, PQ = 2R sin60 = √3R According to Gauss'* law