Question

A closed surface with dimensions a = b = 0.400 m and c = 0.800 m is located as shown in the figure below. The left edge of the closed surface is located at position x = a. The electric field throughout the region is non- uniform and given by E = [(5.00xy)i + (5.00x2y)j ] N/C, where y is in meters. 3) Calculate the net electric flux leaving the closed surface. 4) What net charge is enclosed by the surface?

Answer 1

Soly: a = b =0.4oom Grêven dimensions C = 0.800m The electric field is & = [ (500xy) î + (5.00 27 F NC x=a it c- 66/ we know that the electionc flux 4 = E. do (3) Therefore, total electric flux home [12:20) The couple 0.60368) + Paper Cray) *10.0*** *** - 0 + 0 + 1 (sam kusty3503) + - siggissey + 2 (481+ 5 (+57 35 4 cái) night front dzdy I first two terms 1. - 7. & co are zero due to 7

greate plac) р -gug - - - 50 - 57 Izdy + 5x ly dydt + 5y1 g drey + 5x / grey dz + sofrendt po (left) to cright) zco, tup) (5) x dada 20 (down) ) (les 0 xea --540) +56)*1* | late) -5x0 1 x andy + 5xa 2 2-0 -5 (0.400) x1x1 + 5 (0.400 +0.870 ) x 1x1 + 5*(0.400) [(o40 1920) ( = – 0.6666 + 2 + 1.10934 = 2.44274 = 2.44 Nmale Therefore, the net electric surface is 2.44 Nm/c . flux leaving the closed ) from, Gauss's law Electric flux &- where, & is the and to in the we have a total charge enclosed. permittivity of free space (8.854x0" / so ф. хео total - 2.44 x 8.8548101 = 2.16*10 c Therefore, not charge enclosed by the surface is 2.16x101 -