Find the equivalent capacitance across $A$ $\&$ $B$ ……..$\mu f$

In infinite long uniformly charged string is placed along $z-$ axis. Its linear charge density is $\lambda $. A point charge $q$ is moved from position $(a, 0, 0)$ to $(2a, 0, 0)$ then work done will be

A parallel plate capacitor with air between the plates has a capacitance of $9\, pF$. The separation between its plates is $'d'$. The space between the plates is now filled with two dielectrics. One of the dielectrics has dielectric constant $K_1=3$ and thickness $\frac{d}{3}$ while the other one has dielectric constant $K_2 = 6$ and thickness $\frac{2d}{3}$ . Capacitance of the capacitor is now………$pF$

Electrostatic field of a long uniformly charged wire varies with distance $(r)$ according to relation

Three identical uncharged metal spheres are at the vertices of an equilateral triangle. One at a time, a small sphere is connected by a conducting wire with a large metal sphere that is charged. The center of the large sphere is in the straight line perpendicular to the plane of equilateral triangle and passing through its centre (see figure). As a result, the first small sphere acquires charge $q_1$ and second charge $q_2 (q_2 < q_1)$ . The charge that the third sphere $q_3$ will acquire is (Assume $l >> R$ , $l >> r$ , $d >> R$ , $d >> r$ )