Calculate the number of electrons in one coulomb of negative charge.

Consider two point charges q₁ and q₂ at rest as shown in the figure.

They are separated by a distance of 1m. Calculate the force experienced by the two charges for the following cases:
(a) q₁ = +2μC and q₂ = +3μC
(b) q₁ = +2μC and q₂ = -3μC
(c) q₁= +2μC and q₂ = -3μC kept in water (ε_r = 80)

Two small-sized identical equally charged spheres, each having mass 1 g are hanging in equilibrium as shown in the figure. The length of each string is 10 cm and the angle θ is 30° with the vertical. Calculate the magnitude of the charge in each sphere. (Take g = 10 ms⁻²)

Calculate the electrostatic force and gravitational force between the proton and the electron in a hydrogen atom. They are separated by a distance of 5.3 x 10^–11 m. The magnitude of charges on the electron and proton are 1.6 x 10^–19 C. Mass of the electron is m_e = 9.1 x 10^–31 kg and mass of proton is m_p = 1.6 x 10^–27 kg.

Consider four equal charges q₁, q₂, q₃ and q₄ = q = +1 μC located at four different points on a circle of radius 1m, as shown in the figure. Calculate the total force acting on the charge q₁ due to all the other charges.