A hollow cylindrical box of length 1m area of cross-section `25 cm^(2) ` is placed in a three dimensional coordinate system as shown in the electric field in the region is given
by ` oversetto E = 50 x hati , `where E is in ` N C^(-1) ` and x is in metres . Find
(i) Net flux through the cylinder.
(ii) charge enclosed by the cylinder.
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Explanation

As electric field `oversetto E = 50 x hat I N C^(-1) ` is along +ve direction of X - axis, hence flux passing through side faces 1 and 2 of cylinder is ` phi_1 =E_1 ` A inward and ` phi_2 =E_2` A outward . However , there is no flux associated with curved surface of cylinder.
` therefore " " phi_1 =-E_1 A = - (50 xx 1) xx 25 xx 10^(-4) N m^(2) C^(-1) =- 0.125 N m^(2) C^(-1) `
and ` " " phi_2 =+ E_2A =+ ( 50 xx 2) xx 25 xx 10 ^(-4) N m^(2) C^(-1) =+ 0.250 N m^(2) C^(-1) `
` therefore ` Net electric flux through cylinder
` " " phi_in =phi_1 +phi_2 =-0.125 +0.250 =+ 0.125 N m^(2) C^(-1) `
(b) As net flux `f_in =(q)/( in_0) , `hence charge enclosed by the cylinder will be
` " " q= in _0 . Phi_in =( 8.85xx 10 ^(-12) ) xx 0.125 = 1.1 xx 10^(-12) C = 1.1 pC `