Question

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.

(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.