19 The electrostatic force on a small sphere of charge 0.4𝜇 Cdue to another small sphere of charge - 0.8 𝜇 Cin air is 0.2 N. 1. What is the distance between the two spheres? 2. What is the force on the second sphere due to the first? 20 A charge Q is distributed uniformly over a metallic sphere of radius R. Obtain the expressions for the electric field (E) and electric potential (V) at a point 0 x R. Show on a plot the variation of E and V with x for 0 x 2R. 21 What is relaxation time? Derive an expression for resistivity of a wire in terms of the number density of free electrons and relaxation time CBSE CLASS 12TH

This seems like a complex set of questions related to physics. Let's break it down:

1. The distance between the two spheres can be calculated using Coulomb's Law, which states that the force between two charges is directly proportional to the product of their charges and inversely proportional to the square of the distance between them. The formula is F = k * q1 * q2 / r^2, where F is the force, k is Coulomb's constant (8.99 * 10^9 N m^2/C^2), q1 and q2 are the charges, and r is the distance. We can rearrange the formula to solve for r: r = sqrt(k * q1 * q2 / F). Plugging in the given values, we get r = sqrt((8.99 * 10^9 N m^2/C^2) * (0.4 * 10^-6 C) * (-0.8 * 10^-6 C) / 0.2 N) = 0.03 m or 3 cm.

2. According to Newton's third law, the force on the second sphere due to the first is equal and opposite to the force on the first sphere due to the second. Therefore, the force is -0.2 N.

The other questions require more detailed explanations and derivations.

20. The electric field and potential due to a uniformly charged sphere can be derived using Gauss's law and the definition of electric potential. The electric field inside the sphere (0 < x < R) is E = Q * x / (4 * π * ε0 * R^3), and outside the sphere (x > R) is E = Q / (4 * π * ε0 * x^2). The electric potential inside the sphere is V = Q / (4 * π * ε0 * R), and outside the sphere is V = Q / (4 * π * ε0 * x). The plot of E and V versus x would show E increasing linearly from 0 to R, then decreasing as 1/x^2, and V constant from 0 to R, then decreasing as 1/x.

21. Relaxation time is the average time between collisions for a free electron in a conductor. The resistivity of a wire can be derived from Ohm's law and the definition of current density. The formula is ρ = m / (n * e^2 * τ), where ρ is the resistivity, m is the mass of an electron, n is the number density of free electrons, e is the charge of an electron, and τ is the relaxation time.