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The diagram shows three infinitely long ...

The diagram shows three infinitely long uniform line charges placed on the `X, Y` and ` Z` axis . The word done in moving a unit positive charge from (1,1,1) to (0 , 1,1,) is equal to
.

A

` ( lambda ln2 ) / 2 pi varepsilon _(0)`

B

`(lambda ln 2 ) // pi varepsilon _(0)`

C

`(3lambdal ln 2) //2 pivarepsilon _(0)`

D

None

Text Solution

Verified by Experts

The correct Answer is:
B
Displacement is only along x-axis
`Delta =- underset (1) overset (3) (Ò)E_(x) dx`
` E_x ` is field due to dharged wire lying along y-axis
`E_(x) =(2K(3lambda))/(x) +(2K(lambda))/(x)rArr E_(x) =(2K(lambda))/(x)xx4`
`E_x = (2lambda) (pi in_0 x)` ….(2)
From (1) and (2) `Delta V =- underset (1) overset (2) (Ò) (1l)/(phat I_0 x) dx`
`Delta V = (2 lambda)/(pi in_(0)) [ln x]_(1)^(2) rArrDelta V =(2 lambda)/(piin_(0)) ln1`
`DeltaV=(lambda)/(pi in_(0)) ln2`
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