Question

Two charges A (charge q) and B (charge 2q) are located at points (0, 0) and (a, a) respectively. Let î and ĵ be the unit vectors along x-axis and y-axis respectively. Find the force exerted by A on B, in terms of î and ĵ.

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 :

(i) An electric dipole (dipole moment p = pî), consisting of charges − q and q separated by distance 2a, is placed along the x-axis, with its centre at the origin. Show that the potential V, due to this dipole, at a point x, (x >> a) is equal to (1/4πε₀) · (p·î/x²). (ii) Two isolated metallic spheres S₁ and S₂ of radii 1 cm and 3 cm respectively are charged such that both have the same charge density (2/π × 10⁻⁹) C/m². They are placed far away from each other and connected by a thin wire. Calculate the new charge on sphere S₁.

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 :