Question

Question 8 2 pts An electric field given by E = 2x y2 i + yx?j + 3 zy? k pierces the Gaussian cube shown below. How much charge, in nC, is enclosed in the cube? (E is in N/C,,y and zin meters). Take En = 8.85 x 10-12 C2/Nm2. y (1,3,0) (4,3,0) (1,3,3) (4, 3, 3) (4,0,0) x (1,0,3) (4,0.3) Equations: I enclosed =o total +0 left +0 from bottom top back right E = 8.85 x 10-12 Nm Ф top bottom front = jĒ - dx dz j; -JĒ-dx dy  Q - Ē. dx dz j; = ſ Ē. dy dz î = SĒ - dx dy ź -JĒ- dy dz î Φ back right left

Answer 1

E : 2xy2 i + yx2 + 3 zy2R Genc. E. Eo = 8.85x10-12 C²/N-m2 (i) Prep = { . dx dzi - S(2xy-i +yx-i +3zy=k).(tx dzi) 4 3 S / yx?dx.dz 2:14 y = 3 [constant) Z:03 el 0 3 Z I (43_1).3 Stop - 189 Nl-m% Gi) dobottom =-SE. dx dz į -Syx²dedz y=0 (constant) x:14 Z: 03 o bottom nm tc > Pesant - SE.dkdy R = lexpi + ye+i +32°F).dndyr Pfront = // 3 zy? dedy z = 3 (Constant) x: 14 y : 0-3

Port = 3.361* rady 3.(4-1) (39 & front = 243 rl-m/ Gry Poutton " back = -(E. chudy A - S/3zy?dx dy & Back 2=0 Cconstant) X: 14 y : 0-3 To Back =0 Nm% (v) Pright x = 4 cconstant) 4:03 Z: 0-3 O Pright = f E. dydz st 2x42 dydz **11 [93]* [z]. Pright : 216 N-m/c = 2x4 y²dydz - (vi) Piest = -(E. dydzi Prest -- 32 2 uy 2 dydz Dest :-2x1[*]*[]. Prest -- 54 Nimic x = 1 (Const.) 9:03 O 2:03

o total 11 Genc Co Genc. Protel & Co Pene. = (189 +0+243 +0 +216-54) (8.85x10-12) Gene 5.256 X10-90 Jene 5.256 NC = 2A, Vams 150 Volt Irms W = 500 rad/sec. C=loouf = 100x10-6f R = Gor Vines = √ R² + (XL-XcJ² Z- Irms Vrms 2 => R² + (W L - L oce Irms 150 2 >> Vrms Irms. R² L = Nrms (col- oc) co] [ICE")=6V + Goxoxo) put all values. 500 = 0.13H L = 130mH