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the linear charge density of a thin meta...

the linear charge density of a thin metallic rod varies with the distance `x` from the end as `lambda=lambda_(0)x^(2)(0 le x lel)` The total charge on the rod is

A

`(lambda_(0)l^(3))/(3)`

B

`(lambda_(0)l^(3))/(4)`

C

`(2lambda_(0)l^(3))/(3)`

D

`(lambda_(0)l^(3))/(2)`

Text Solution

Verified by Experts

The correct Answer is:
A

`dQ=lambda(dx)=lambda_(0)x^(2)(dx)`
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Knowledge Check

  • If linear charge density of a wire as shown in the figure is lambda

    A
    potential at the centre is `(lambda)/(2 epsi_(0))`
    B
    electric field at the centre of the loop is `(lambda)/(2 pi epsi_(0)R)`
    C
    electric field at the centre of the loop is `(lambda)/(2 pi epsi_(0)R) + (lambda)/(2 epsi_(0)R)`
    D
    None of the above

  • The linear charge density of a uniform semicircular wire varies with theta shown in the figure as lambda=lambda_(0)costheta if R is the radius of the loop ,of the charge on the wire is

    A
    `lambda_(0)R`
    B
    `3lambda_(0)R`
    C
    `(2lambda_(0)R)/(3)`
    D
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