Question

2 Consider a toy model of an atomic nucleus. In this picture, a proton is considered to move through a uniform sphere of charge (p 1)e, where p is the number of protons in the nucleus and e is the charge on the proton. The radius of the nucleus is given by the formula In the above A is the atomic mass number (protons plus neutrons) and ro 1.3 × 10-15 m. For this model, find the force on a proton as it moves from the center of the nucleus out to the edge.

Answer 1

Force on charge = q * E^vector q rightarrow charge (e) we need to find electric field (E^vector) inside a solid sphere with uniform charge distribution as function of distance from centre. Let the charge density per unit volume be eta [Total charge/Total volume = (p - 1)e/4/3 pi R^3 = eta]^* where R = r_0 A^1/3 E^vector inside a solid sphere of radius 'R' E_inside^vector = Q times r/4 pi epsilon_0 R^3 (r < R)^* substituting values Q = (P - 1)e R = r_0 A^1/3 E_inside^vector (as function of distance from centre) = (P - 1) * e * r/4 pi epsilon_0 A * r_0^3 force as function of distance r, (r < R) f^vector = q * E^vector implies e * (P - 1) * e * r/4 pi epsilon_0 A * r_0^3 force^vector = (P - 1) e^2 * r/4 pi epsilon_0 A * r_0^3 Ans