(8%) Problem 8: A Gaussian surface in the shape of a rectangular box is centered at the origin, and its edges are parallel to the coordinate axes. Edges parallel to the x axis have length a, edges parallel to the y axis have length b; edges parallel to the axis have length c. A uniform and constant electric field E = Exi + Eyj + Ek fills the region of space which contains the rectangular box. x 2 b a C Y 6% Part (a) Enter an expression for the outward-pointing normal vector on the front face of the box, n front front = Correct! A 6% Part (b) Enter an expression for E-dA on the front face of the rectangular box. For the magnitude of dA use dA. 6% Part (c) Perform a flux integral over the front face of the box to obtain the outward electric flux, PE,front, through this one face. DE,front 4 Ex b c = dA 7 ^^4 852 96 3 HOME + 0 K a b Ex * 1 Ey Ez P + 0 END X y Z VO BACKSPACE DEL CLEAR Submit Hint Feedback I give up! Grade Summary Deductions Potential Submissions 2% 98% Attempts remaining: 4 (2% per attempt) detailed view 2% Hints: 2% deduction per hint. Hints remaining: 1 Feedback: 2% deduction per feedback. 6% Part (d) Enter an expression for the outward-pointing normal vector on the back face of the box, back 1 back = X Attempts Remain A 6% Part (e) Enter an expression for E-dA on the back face of the rectangular box. For the magnitude of dA use dA. A 6% Part (f) Perform a flux integral over the back face of the box to obtain the outward electric flux, PE.back, through this one face. A 6% Part (g) Enter an expression for the outward-pointing normal vector on the right face of the box, right A 6% Part (h) Enter an expression for E-dA on the right face of the rectangular box. For the magnitude of dA use dA. 6% Part (i) Perform a flux integral over the right face of the box to obtain the outward electric flux, PE,right, through this one face. 6% Part (j) Enter an expression for the outward-pointing normal vector on the left face of the box, n left A 6% Part (k) Enter an expression for E.dA on the left face of the rectangular box. For the magnitude of dA use dA. A 6% Part (1) Perform a flux integral over the left face of the box to obtain the outward electric flux, PE,left, through this one face. 6% Part (m) Perform a flux integral over the top face of the box to obtain the outward electric flux, PE,top, through this one face. A 6% Part (n) Perform a flux integral over the bottom face of the box to obtain the outward electric flux, PE,bottom, through this one face. A 6% Part (0) Enter an expression, reduced to its most simple form, for the electric flux through the entire closed box, DE,box A 6% Part (p) Enter an expression, reduced to its most simple form, for the net charge, Qenclosed, contained inside the closed box.