Problem 2: An early model of the atom, proposed by Rutherford after his discovery of the atomic nucleus, had a positive point charge +Ze (the nu- cleus) at the center of a sphere of radius R with uniformly distributed neg- ative charge -Ze. Z is the atomic number, the number of protons in the nucleus and the number of electrons in the negative sphere. Show that the electric field strength inside this atom is Ein = Ze 1 4περ \r2 R³ a) Fig.2 illustrates the model of the atom. In the figure, draw the Gaussian surface that you will use to find the field. Draw the vectors that represent the electric field at the Gaussian surface. How do you know the direction of the electric field inside the atom? q=ze R Ze ง P- FIG. 2: The scheme for Prob- lem 2 b) What is the volume charge density p. of the negative sphere? Use Gauss's law and the symmetry arguments in order to find the expression for the electric field strength inside the atom. What is the electric field strength outside this atom? c) A uranium atom has Z = 92 and R = 0.10 nm. What is the electric field strength at r = R/2?

Problem 2: An early model of the atom, proposed by Rutherford after his discovery of the atomic nucleus, had a positive point charge +Ze (the nu- cleus) at the center of a sphere of radius R with uniformly distributed neg- ative charge -Ze. Z is the atomic number, the number of protons in the nucleus and the number of electrons in the negative sphere. Show that the electric field strength inside this atom is Ein = Ze 1 4περ \r2 R³ a) Fig.2 illustrates the model of the atom. In the figure, draw the Gaussian surface that you will use to find the field. Draw the vectors that represent the electric field at the Gaussian surface. How do you know the direction of the electric field inside the atom? q=ze R Ze ง P- FIG. 2: The scheme for Prob- lem 2 b) What is the volume charge density p. of the negative sphere? Use Gauss's law and the symmetry arguments in order to find the expression for the electric field strength inside the atom. What is the electric field strength outside this atom? c) A uranium atom has Z = 92 and R = 0.10 nm. What is the electric field strength at r = R/2?