A charge particle q is shifted from point 1 to point 2 in the electric field of a straight long linear charge of `lambda`.
i. Find the electric work done if `r_1 = R` and `r_2 = 2 R`
ii. Find the potential difference between 1 and 2.
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Explanation

(i) The work done by the electric field is
`W_(e 1) = int vec F_(e 1). vec d l = qint vec E .vec d l`
`q int ((lambda)/(2 pi epsilon_0 r) hat r) . (d r hat r) = (lambda q)/(2 pi epsilon _0) int _(r = R)^(r = 2 R) (d r)/(r) = (lambda q)/(2 pi epsilon _0) ln 2`.
(ii) `V_2 - V_1 = (W_(ext))/q = (((lambda q)/(2 pi epsilon_0) ln 2))/q = (lambda)/(2 pi epsilon_0) ln 2`