At t = 0 we have a spherical cloud of radius R and total charge Q, comprising N point-like particles, where N is a large mumber. Each particle haN charge q = Q/N and mass m. The particle density is uniform, and all particles are at rest. (a) Evaluate the clectric field at r< R and the eloctrostatic potential energy of the system. (b) Due to the Coulomb repulsion, the cloud bogins to expand radially, koeping its spherical symmetry. Assume that the particles do not overtake one another, i.c., that if two particles were initially located at ri (0) and r2(0), with r2(0) > r1(0), then r2(t) > ri(t) at any subsoquent. time t > 0. Consider the particles located in the infinitesimal spherical shell ro < r, < ro + dr, with ro + dr < R, at t = 0. Show that the equation of motion of the layer is dr, (1)

At t = 0 we have a spherical cloud of radius R and total charge Q, comprising N point-like particles, where N is a large mumber. Each particle haN charge q = Q/N and mass m. The particle density is uniform, and all particles are at rest. (a) Evaluate the clectric field at r< R and the eloctrostatic potential energy of the system. (b) Due to the Coulomb repulsion, the cloud bogins to expand radially, koeping its spherical symmetry. Assume that the particles do not overtake one another, i.c., that if two particles were initially located at ri (0) and r2(0), with r2(0) > r1(0), then r2(t) > ri(t) at any subsoquent. time t > 0. Consider the particles located in the infinitesimal spherical shell ro < r, < ro + dr, with ro + dr < R, at t = 0. Show that the equation of motion of the layer is dr, (1)