Electric Flux

A disk of radius with uniform positive charge density is placed on the plane with its center at the origin. The Coulomb potential along the -axis is .
A particle of positive charge is placed initially at rest at a point on the axis with and . In addition to the Coulomb force, the particle experiences a vertical force with Let . Which of the following statement(s) is(are) correct?

A charge is kept at the central point P of a cylindrical region. The two edges subtend a half-angle at P, as shown in the figure. When , then the electric flux through the curved surface of the cylinder is . If , then the electric flux through the curved surface becomes , where the value of n is______.

 

A small electric dipole , having a moment of inertia about its center, is kept at a distance from the center of a spherical shell of radius . The surface charge density is uniformly distributed on the spherical shell. The dipole is initially oriented at a small angle as shown in the figure. While staying at a distance , the dipole is free to rotate about its center. If released from rest, then which of the following statement(s) is(are) correct?
\includegraphics[width=0.4\linewidth]{ph5.png}

A charge is kept at the central point of a cylindrical region. The two edges subtend a half-angle at , as shown in the figure. When , then the electric flux through the curved surface of the cylinder is . If , then the electric flux through the curved surface becomes , where the value of is \_\_\_\_. \includegraphics[width=0.3\linewidth]{ph8.png}