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 arc $$PQ$$ 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 statement is (are) true?

A point charge $$+Q$$ is placed just outside an imaginary hemispherical surface of radius $$R$$ as shown in the figure. Which of the following statements is/are correct?

The figures below depict two situations in which two infinitely long static line charges of constant positive line charge density $$\lambda $$ are kept parallel to each other. In their resulting electric field, point charges $$q$$ and $$-q$$ are kept in equilibrium between them. The point charges are confined to move in the $$x$$ direction only. If they are given a small displacement about their equilibrium positions, then the correct statement(s) is (are)

A parallel plate capacitor has a dielectric slab of dielectric constant $$K$$ between its plates that covers $$1/3$$ of the area of its plates, as shown in the figure. The total capacitance of the capacitor is $$C$$ while that of the portion with dielectric in between is $${C_1}.$$ When the capacitor is charged, the plate area covered by the dielectric gets charge $${Q_1}$$ and the rest of the area gets charge $${Q_2}.$$ The electric field in the dielectric is $${E_1}$$ and that in the other portion is $${E_2}.$$ Choose the correct option/ options, ignoring edge effects.