Imagine an infinite plane of charged nonconducting ice cream. Let this plane hav
ID: 2989552 • Letter: I
Question
Imagine an infinite plane of charged nonconducting ice cream. Let this plane have a nonzero thickness of d = 0.40 m, and a uniform volume charge density of ? = 84nC/m3. Lactose intolerant students may imagine a nondairy ice cream alternative, but please ensure that it is still nonconducting and has the same charge density.
Find the electric field everywhere. We are mostly concerned with the region inside the plane itself. That is to say, if we align our xy plane with the infinite plane and letz=0 at the center of the plane, we are most concerned with |z|<d/2.
What is Ez at z = 0.07 m?
Ez(0.07 m) = N/C
How about in the center of the plane?
Ez(0 m) = N/C
Now add an infinitely thin charged cookie layer to the top and bottom of this plane, making an infinite ice cream sandwich. Let this skin have a surface charge density of ? =?16.8 nC/m2. The surface charge density has been carefully engineered so as to make the electric field outside the sandwich exactly zero while leaving the electric field inside the sandwich unchanged from your calculations in part a. We encourage you to verify this fact if you would like extra practice.
What is the potential everywhere in space? In particular, what is the potential at z =0.07 m? Let the potential be zero far away from the sandwich.
V(0.07 m) = kV
How about at the center of the plane?
V(0 m) = kV
What is the energy stored in a chunk of this infinite sandwich with cross sectional area A = 1.5 m2?
U = J
EXPLAIN THE STEPS!
Explanation / Answer
Use gauss' theorem to find the electric field at the different points.
The field produced outside will be equal to (by using cylidrical gaussian surface) =
(sigma/ 2*epsilon)
where sigma=84*0.4 nC/m2
thus E comes to be 1897 N/C
similarly constructing gaussian surfaces with one face at z=0.07 and other outside and knowing electric field outside
E at z=0.07 comes to be 0.3*1897 = 569.1 N/C
Similarly solving E at z=0 is 0.
In the second half as the electric field is 0 outside, the poential will be constant outside and thus will be 0 at the surface of the sandwich. The electric field inside will be (1897/0.2)*x. Integrate to find the change, it is 166.46 V. Thus it is potential at 0.07m and similarly 189.7 V at z=0.
Energy stored is 0.5*epsilon*E^2, find using E calculated above