Question

An infinitely long thin non-conducting 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 the are $PQ$ subtends an angle ${120}^{\circ }$ at the center $O$ of the spherical shell, as shown in the figure. The permittivity of free space is ${\in }_0$ Which of the following statements is (are) true?

• A. The electric flux through the shell is $\sqrt{3}R\lambda /{\in }_0$
• 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 $\sqrt{2}R\lambda /{\in }_0$
• D. The electric field is normal to the surface of the shell at all points

Answer 1

Answer: (A), (B)

The correct options are
A The electric flux through the shell is $\sqrt{3}R\lambda /{\in }_0$
B The z-component of the electric field is zero at all the points on the surface of the shell