Electric field at a point near an infinitely long uniform linear charge
`oint vecE.vec(dA) = int_text(upper surface) vecE.vec(dA)`
` + int_text(curved surface) vecE.vec(dA)`
` + int_text(lower surface) vecE.vec(dA)`
`= int_text(upper surface) E.(dA) cos90^o`
` + int_text(curved surface) E.(dA) cos0^o`
` + int_text(lower surface) E.(dA) cos90^0`
`= 0 + int E dA + 0`
`= E(2pirl)`
From gauss law
`E2pirl = (lambdal) /epsilon_0`
`E = lambda/(2piepsilon_0r)`
` + int_text(curved surface) vecE.vec(dA)`
` + int_text(lower surface) vecE.vec(dA)`
`= int_text(upper surface) E.(dA) cos90^o`
` + int_text(curved surface) E.(dA) cos0^o`
` + int_text(lower surface) E.(dA) cos90^0`
`= 0 + int E dA + 0`
`= E(2pirl)`
From gauss law
`E2pirl = (lambdal) /epsilon_0`
`E = lambda/(2piepsilon_0r)`