Three capacitors of 1\(\mu F\), 2\(\mu F\) and 3\(\mu F\)  are joined in series.
(i) How many times will the capacity become when they are joined in parallel?
(ii) Determine the charge supplied by the battery of 100 V to the maximum resultant capacitor among both the arrangement.

Two charges +Q and -Q are kept at points (-x₂, 0) and (x₁, 0) respectively, in the XY-plane. Find the magnitude and direction of the net electric field at the origin (0, 0).

An electricdipole consists of two opposite charges each of magnitude 1.0\(\times\)10^-6C separated by 2cm. The dipole is placed in an external uniform field of 1\(\times\)10⁵ N/C. Find
(i) the maximum torque exterted by the field on the dipole
(ii) the work which an external agent will have to do in turning the dipole through 180⁰ starting the position, \(\theta\) = 0⁰.

A charge Q is distributed over two concentric hollow shaperes of radii r and R( > r) such that their surface densities are equal. Find the potential at the common centre.

(i) How is the electric field due to a charged parallel plate capacitor affected, when a dielectric slab is inserted between the plates fully occupying the intervening region?
(ii) A slab of material of dielectric constant K has the same area as the plates of a parallel plate capacitor but has thickness \(\frac{1}{2}\) d, where d is the separation between the plates. Find the expression for the capacitance when the slab is inserted between the plates.