Problem 1: An infinite slab of charge of thickness 2zo lies in the xy-plane between z = - zo and z = +zo. The volume charge density p (C/m³) is a positive constant. Find the electric field everywhere and draw the plot of its vertical component. a) Fig.1 shows the Gaussian surface that you may use to find the field everywhere inside the slab (in the region -zo ≤ z ≤ zo). In Fig.1, draw vectors that indicate the direction of the electric field in the slab (the slab is positively charged). Which parts of the Gaus- sian surface make zero contribution to the electric flux? Does the Gaussian surface have to be symmetric with respect to the z = = 0 (horizontal) plane? Explain why. Gaussian surface Zo 리 -Zo A FIG. 1: The scheme for Problem 1 b) Use Gauss's law and the symmetry arguments to find an expression for the electric field strength inside the slab as a function of z. Write down the field E in vector (component) form both above and below 0 plane. the z = c) In Fig.1, draw the Gaussian surface that should be used to find the electric field outside the slab (pay attention to the symmetry). Use Gauss's law to find the field and express it in vector form both above and below the slab. d) Draw a graph of the z-component (not the magnitude) of the electric field, Ez, for the values of z from -2zo to 2zo.

Problem 1: An infinite slab of charge of thickness 2zo lies in the xy-plane between z = - zo and z = +zo. The volume charge density p (C/m³) is a positive constant. Find the electric field everywhere and draw the plot of its vertical component. a) Fig.1 shows the Gaussian surface that you may use to find the field everywhere inside the slab (in the region -zo ≤ z ≤ zo). In Fig.1, draw vectors that indicate the direction of the electric field in the slab (the slab is positively charged). Which parts of the Gaus- sian surface make zero contribution to the electric flux? Does the Gaussian surface have to be symmetric with respect to the z = = 0 (horizontal) plane? Explain why. Gaussian surface Zo 리 -Zo A FIG. 1: The scheme for Problem 1 b) Use Gauss's law and the symmetry arguments to find an expression for the electric field strength inside the slab as a function of z. Write down the field E in vector (component) form both above and below 0 plane. the z = c) In Fig.1, draw the Gaussian surface that should be used to find the electric field outside the slab (pay attention to the symmetry). Use Gauss's law to find the field and express it in vector form both above and below the slab. d) Draw a graph of the z-component (not the magnitude) of the electric field, Ez, for the values of z from -2zo to 2zo.