A long circular tube of length `10 m` and radius ` 0.3 m` carries a current `I` along its curved surface as shown . A wire - loop of resistance `0.005 ohm` and of radius `0.1 m` is placed inside the tube its axis coinciding with the axis of the tube . The current varies as `I = I_(0)cos(300 t)` where `I_(0)` is constant. If the magnetic moment of the loop is `Nmu_(0)I_(0) sin (300 t)`, then 'N' is

Answer

`6.`

Explanation

Flux through circular ring
`phi = ((mu_(0)I)/(L)) pir^(2) rArr phi= (mu_(0))/(L) pir^(2)I_(0) css 300t`
Current in the ring `I = (1)/(R ) (dphi)/(dt)`
`i = (mu_(0)pi r^(2)I_(0))/(RL)* sin 300t xx 300`
`= mu_(0)I_(0) sin 300t [(pir^(2)* 300)/(RL)]`
`M = I* pi r^(2) = mu_(0)I_(0) sin 300t [(pi^(2)r^(4)* 300)/(RL)]`
Taking `pi^(2) = 10`,we get
`M = 6mu_(0)I_(0)sin 300t`
Thus `N = 6`