A slab of insulating material has a uniform positive charge density ? , as shown

Question

A slab of insulating material has a uniform positive charge density ?, as shown in the figure below. The slab is infinite in the y and z directions.

Derive expressions for the field for the following regions. (Use the following as necessary: ?0, ?, d, and x as necessary.)     (a) the exterior regions (x >

in which      direction?
    
     (b) the interior region of the slab (0 < x < d/2)

in which      direction     
    Note: your answers should be the same when x = d/2

d 2 A slab of insulating material has a uniform positive charge density ?, as shown in the figure below. The slab is infinite in the y and z directions. Derive expressions for the field for the following regions. (Use the following as necessary: ?0, ?, d, and x as necessary.) (a) the exterior regions (x > in which direction? the interior region of the slab (0

Explanation / Answer

Take a can (like one used for canned peaches) and send it through the plane of charge so that the bottom and top of the can are parallel to the plane of charge.

Now the electric flux through the can is (by gauss's law) the Integral[Dot[E,da]] where E is the electric field and da is the differential surface area is equal to 2*Pi*r^2 *E which is also equal to Q/e that is the enclosed charge divided by epsilon. But remember Q=2*pi*r^2 * d *rho.

The rest of the algebra is trivial

E=rho*d/(2e) facing in the x direction

PS. Use a symmetry argument to convince yourself that E is uniform along the top and bottom of the can and E is perpindicular to the top and bottom of the can

Oh, just realizeed i made a mistake.....
My bad,
The thickness of your charge is 2*d not just d . E=rho*d/e facing in the x direction.

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