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Use Gauss'law to derive the expression f...

Use Gauss'law to derive the expression for the electric field ` (oversetto E) ` due to a straight uniformaly charged infinite line of charge density `lambda C 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 distance ` r_1 to r_2 (r_2 lt r_1) `

Text Solution

Verified by Experts

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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