15.. The diagram below shows a conducting slab that extends infinitelyr far towards both the top and bottom of the diagram. (3 ."j' 1". :4 #P I II '._-'_I_ in: Conductor ll+:r The right side of the slab bears a positive surface charge density. or. The diagram aLso shows the cross section of a cube-shaped Gaussian surface. Each edge of the cube has length L. Assume that the cube is centered so that half of it lies within the conducting slab and half lies on the outside. The sides of the cross section of the cube are numbered 1 through 15. where the top and bottom sides are each divided into the portion inside and the portion outside of the conducting slab. 1. The definition of electric flux is o=fa For each side of the Gaussian surface in the table below: I indicate the direction of the electric field by the charged slab, I indicate the the direction of the infinitesimal area vector, {IA , and I write an ex-ression for the electric flux in terms of E and L. Side of Direction of _* Gaussian Electric Field by Directfn 5f dA Electric Flux surface the Slab 2. In the table above, you only considered the sides of the Gaussian surface's cross section shown in the diagram. However, the Gaussian surface is a three dimensional cube, not a two dimensional square. Write expressions for the electric flux through the front side of the box and through the back side of the box in terms of E and L. Flux through front of Gaussian surface = I l Flux through back of Gaussian surface = I | 3. Write an expression for the net flux through all sides of the Gaussian surface in terms of E and L. Net flux through all sides of the Gaussian surface = I I 4. Write an expression for the amount of charge contained within the Gaussian surface in terms of o' and L. Charge enclosed by Gaussian surface = I 5. apply Gauss's Lam.r to derive an expression for the magnitude of the electric field at point P in terms of the surface charge, or , and the constant 50. Electric Field at F' = |