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Use Gauss'law to derive the expression for the electric field(oversetto E)due to a straight uniformaly charged infinite line of charge density lambdaC m ^(-1) (b) Draw a graph to show the variation of E with perpendicular distance r from the line of charge. (c) Find the work done is bringing a charge q from perpendicular distancer_1 to r_2 (r_2 lt r_1) |
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Answer» Solution :Elementary work done against the electric field for bringing a charge q SITUATED at a normal distance .r. from the line of charge is given by: `dW =- FDR =- q E dr =- q [(lambda)/( 2 pi in _0 r) ] dr ` ` therefore ` Work done in bringing the charge q from perpendicular distance `r_1 "to" r_2 ` is given as : `W= INT dW =- underset (r_1) oversetto (r_2) int (q lambda)/( 2 pi in _0 r)dr = -(qr)/( 2 pi in _0)[1N r ]_(r_1) ^(r_2)=-( q lambda)/( 2 pi in _0) 1n (r_2)/(r_1)=(q lambda )/( 2 pi in _0)1n ((r_1)/( r_2_)) ` |
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