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 E_z = 0
Length, PQ = 2R sin60 = √3R According to Gauss's law

Answer 2

field due to straight wire is perpendicular to the wire i e in x direction so z component of the electric field is zero