A slab of insulating material of uniform thickness d, lying between ?d/2 to +d/2

Question

A slab of insulating material of uniform thickness d, lying between ?d/2 to +d/2 along the x axis, extends infinitely in the y and z directions, as shown in the figure. The slab has a uniform charge density ?. The electric field is zero in the middle of the slab, at x=0.

Which of the following statements is true of the electric field E?  at the surface of one side of the slab?

Which of the following statements is true of the electric field  at the surface of one side of the slab?

its a multi-part that won't show until this is answered...

A.) The direction of E?  is constant but its magnitude varies across the surface. B.) Both the magnitude and the direction of E?  are constant across the entire surface. C.) The direction of E?  varies across the surface but its magnitude is constant. D.) Both the magnitude and the direction of E?  vary across the surface.

Explanation / Answer

Here ,

for the slab , as it is infinitely long

but the thickness is limited

For the electric field at the surface of one side

due to symmetry ,

the magnitude and direction of electric field at all the points on the side will be same

the correct option is

B.) Both the magnitude and the direction of E  are constant across the entire surface.

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