A flat slab of nonconducting material has thickness 2d, which is small compared to its other...

 

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A flat slab of nonconducting material has thickness 2d, which is small compared to its other dimensions. Define the x axis to be along the direction of the slab's thickness, with the origin at the center of the slab. If the slab has a uniform charge density p(x)=-po in the region -d<x<0, and p(x)=+po in the region 0<x<d, determine the electric field E(x) in the region (a) -d<x<0, and (b) 0<x<d. (Hint: The electric field must be zero everywhere outside of the slab, since the fields from the left and right sides of the slab must cancel there. Draw Gaussian surfaces that are partly inside the slab and partly outside.) Your expressions for E should follow the convention that E>0 for a field to the right, and E<0 for a field to the left. A flat slab of nonconducting material has thickness 2d, which is small compared to its other dimensions. Define the x axis to be along the direction of the slab's thickness, with the origin at the center of the slab. If the slab has a uniform charge density p(x)=-po in the region -d<x<0, and p(x)=+po in the region 0<x<d, determine the electric field E(x) in the region (a) -d<x<0, and (b) 0<x<d. (Hint: The electric field must be zero everywhere outside of the slab, since the fields from the left and right sides of the slab must cancel there. Draw Gaussian surfaces that are partly inside the slab and partly outside.) Your expressions for E should follow the convention that E>0 for a field to the right, and E<0 for a field to the left.

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