Question

A parallel plate capacitor is an arrangement of two identical metal plates kept parallel, a small distance apart. The capacitance of a capacitor depends on the size and separation of the two plates and also on the dielectric constant of the medium between the plates. Like resistors, capacitors can also be arranged in series or parallel or a combination of both. By virtue of electric field between the plates, charged capacitors store energy.

Two charges q₁ and q₂ are placed at the centres of two spherical conducting shells of radius r₁ and r₂ respectively. The shells are arranged such that their centres are d [> (r₁ + r₂)] distance apart. The force on q₂ due to q₁ is :

Coulomb force F versus 1/r² graphs for two pairs of point charges (q₁ and q₂) and (q₂ and q₃) are shown in the figure. The ratio of charges q₁/q₃ is :

Three small charged spheres X, Y and Z carrying charges + q, – q and + q respectively are placed equidistant from each other, as shown in the figure. The spheres Y and Z are held in place. Initially X is also held in place, but is otherwise free to move. When X is released, the path followed by it will be :