Question

Three point charges q, 2q and nq are placed at the vertices of an equilateral triangle. If the potential energy of the system is zero, find the value of n.

State Gauss's Law in electrostatics. Apply this to obtain the electric field E at a point near a uniformly charged infinite plane sheet.

Two long straight wires 1 and 2 are kept as shown in the figure. The linear charge density of the two wires are λ₁ = 10 μC/m and λ₂ = − 20 μC/m. Find the net force F experienced by an electron held at point P.

(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.