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An insulting thin rod of length l has a ...

An insulting thin rod of length `l` has a linear charge density `rho(x)=rho_(0)(x)/(l)` on it. The rod is rotated about an axis passing through the origin (x=0) and perpendicular to the rod. If the rod makes n rotations per second, then the time averaged magnetic moment of the rod is :

A

`pi/4 n rho l^(3)`

B

`pi n rhol^(3)`

C

`pi/3 n rho l^(3)`

D

`n rho l^(3)`

Text Solution

Verified by Experts

The correct Answer is:
A
`omega = 2 pi " n rad/s"`
dQ = `rho.dx`
`=(rho_(0))/l x dx `
`dI = (dQ.omega)/(2pi)`

dM = `dI xx A`
`int dM = int_(0)^(1) omega /(2pi)((rho_(0))/l)x.pi x^(2)dx`
`M = (pinrho_(0)l^(3))/4`
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