Question

QUESTIONS 1. (30p)The cylindrical closed surface with radius R length L is placed into a nan uniform electrical filed (Ē = (3x2 + 2)2)) as shown in the figure.; a. (15p) Find the total electric flux passing through the closed surface.. b. (15p) Find the total electric charge inside the closed surface. L È R 2. (40p)A conductive spherical shell of inner radius 2R and outer radius 3R is caries a net charge -3Q. The total charge of an insulating sphere with a radius of the same center as the spherical shell is + 20. Using Gauss' law find the electrical field in the regions; a. r<R b. R<r<2R c. 2R <r <3R d. r > 3R 3R 2R ym) 0,3 -34 3. (30p)The electrical charges -39, 24, 4q, and are located at the coordinates c (0.5; 0.3; 0), e (0.5; 0; 0), f (0.5; 0; 0.3) of the rectangular prism respectively as shown in figure. (Here q=5uC) a. (15p)Find the electrical potential at point A(0,1;0;0) b. (15p)Find the total work required to move charges (m) from infinity to their locations. 0,3 (m)

Answer 1

placed in (a) The electric is QI given Cylinder of length hand Radius R is electric field È = (3x²+2) flux through the close surface of cylinder given by PE = E. dB where ds = surface element 14 uose gauss divergence theorem $E. closed surface a=a+L که. 7. Ê de 8 where de = volume element x=G ve divergence of tz

PE Sz.E de $ E-43 V.F = (be tong g tom k ). (2x+2) * = (37°+2) =6840 مه F ² = 66 so co-ordinate de I gdy do dr 2Ã X-QL x dx = 6 Op E 8=0 0=0 x=a R Atl 2 Pc = for de z6lx de for cylindrical Sxeado de de for de su de = 6 g (2) X 3*R* ((a+L)*a") = 36 R*( a +2°+221 +22) 3*R* ( 1+201 gylindrical surface is Ono Pe E The flax through closed De = ga R" (l+202)

وم (6) To find the total electric charge inside the closed surface ure gauss. law Dene total charge Where lere E enclosed closed closed surface surface So Den = 8 de QE & E. ds by GO Olen ६० de & (37R) ( 2 +224), The fatal enclosed closed surface is charge inside the 3a RE ( + zal) Qen