Problem 3: An infinite plane of charge with surface charge density ŋ = 3.2 μC/m² has a 20-cm-diameter circu- lar hole cut out of it. What is the electric field strength directly over the center of the hole at a distance of 12 cm. + + + + + 12 cm D 275 + + + = + + + + + + P 225 - + + + + + ++ FIG. 3: The scheme for Problem 3 a) The solution is based on the idea that the hole in the plane can be mod- eled as a superposition of the positively and negatively charged surfaces of the same shape, as shown in Fig. 3. On the right panel of Fig. 3, draw the vectors that represent electric fields created at point P by the infinite plane (E+) and the negatively charged disk (E-). Which field has a larger magnitude? Explain why. What is the direction of the total electric field E at point P? b) Find the z-components of the fields E and E. Pay attention to the signs of the components that you get (the field that points down has to have a negative z-component). Compute the total electric field in P as a vector sum E = E + E.

Problem 3: An infinite plane of charge with surface charge density ŋ = 3.2 μC/m² has a 20-cm-diameter circu- lar hole cut out of it. What is the electric field strength directly over the center of the hole at a distance of 12 cm. + + + + + 12 cm D 275 + + + = + + + + + + P 225 - + + + + + ++ FIG. 3: The scheme for Problem 3 a) The solution is based on the idea that the hole in the plane can be mod- eled as a superposition of the positively and negatively charged surfaces of the same shape, as shown in Fig. 3. On the right panel of Fig. 3, draw the vectors that represent electric fields created at point P by the infinite plane (E+) and the negatively charged disk (E-). Which field has a larger magnitude? Explain why. What is the direction of the total electric field E at point P? b) Find the z-components of the fields E and E. Pay attention to the signs of the components that you get (the field that points down has to have a negative z-component). Compute the total electric field in P as a vector sum E = E + E.