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A thin straight infinitely long conducti...

A thin straight infinitely long conducting wire having charge density `lambda ` is enclosed by a cylinder surface of radius r and length l, its axis coinciding with the length of the wire. Find the expression for the electric flux through the surface of the cylinder.

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As shown in a thin straight infinitely long conducting wire having linear charge density `lambda ` is enclosed by a cylinder surface of radius r and length l with its axis coinciding with the length of the wire.
As per Gauss.s law total electric flux through the entire surface of the cylinder
` phi_in =(1)/(in_0) ` (charge enclosed within the cylinder)
` = (1)/(in_0) (lambda l) =(lambda l)/(in_0) `
` (##U_LIK_SP_PHY_XII_C01_E09_022_S01.png" width="80%">
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Knowledge Check

  • a point charge q is placed at the centre of a cylinder of length L and radius R the electric flux through the curved surface of the cylinder is

    A
    `(q)/(epsilon_(0))(L)/(sqrt(L^(2)+R^(2)))`
    B
    `(q)/(epsilon_(0))(L)/(sqrt(L^(2)+2R^(2)))`
    C
    `(q)/(epsilon_(0))(L)/(sqrt(L^(2)+4R^(2)))`
    D
    `(q)/(2epsilon_(0))`

  • A cylinder of radius R and length l is placed in a uniform electric field E parallel to the axis of the cylinder. The total flux over the curved surface of the cylinder is

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    zero
    B
    `piR^2E`
    C
    `2piR^2E`
    D
    `E//piR^2`

  • A cylinder of length L and radius b has its axis coincident with x-axis. The electric field in this region is vecE = 200hati . Find the flux through the left end of the cylinder.

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