Electric field of a uniformly charged square sheet
In this exam, we are going to explore the properties of a uniformly charged square sheet with charge Q = 5 mC and side length a = 3 cm.
(a) Calculate the charge density of the square sheet. Be sure to use the correct symbol to represent charge density (λ, σ, ρ).
(b) Set up your sheet so that it is located in the xy-plane and centered on the origin (as pictured in Figure 1). How have you modeled the sheet using a collection of point charges? Particularly, you must mention:
• How much charge is on each point charge?
• Where are the charges located?
• How many charges have you used? How do you know that this is "enough"?
(c) Before you calculate the field, identify which direction the field will point for test points on the z-axis. (Along î, ĵ, or k̂?) Explain your reasoning.