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Ahollow 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 byoversetto E = 50 x hati , where E is inN C^(-1)and x is in metres . Find (i)Net flux through the cylinder.(ii) charge enclosed by the cylinder.(##U_LIK_SP_PHY_XII_C01_E10_019_Q01.png" width="80%"> |
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Answer» Solution :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 ` |
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