Reference no: EM132229983

Problem - An infinite slab of charge of thickness 10m lies on the x-y plane between z = -5m and z=+5m. The charge density, ρ, is 4 C/m³ and is a constant throughout the slab. (HINT: this is similar to what we did in class to find the E-field for an "infinite sheet" of charge... remember the cookie dough and the cookie cutter).

(a) Use Gauss's Law to find an expression for the Electric Field strength for any point inside the slab (- 5m ≤ z ≤ +5m ). (HINT: Draw a Gaussian "cookie cutter" of thickness 2Z that straddles the x-y plane so that half of the cookie cutter is above the x-y plane and half below (and where Z is an arbitrary length that is less than 5 m high). Remember, in order to apply Gauss's Law, you will have to calculate how much charge that cookie cutter captures inside of it).

(b) Find an expression for the Electric Field strength for any point above or below the slab (|z|≥ +5) (HINT: Draw a Gaussian "cookie cutter" of thickness 2Z that straddles the x-y plane so that half of the cookie cutter is above the x-y plane and half below (and where Z is an arbitrary length that is greater than 5 m high). Remember, in order to apply Gauss's Law, you will have to calculate how much charge that cookie cutter captures inside of it. This will be different than the charge inside of the cookie cutter in part (a)).

(c) Use the graph to sketch the magnitude of E from z = 0m to z = 8m (this same graph would apply to regions from 0m to -4m as well).