A cylindrical cavity of diameter a exists inside a cylinder of diameter `2a` as shown in the figure. Both the cylinder and the cavity are infinitity long. A uniform current density `j` flows along the length . If the magnitude of the magnetic field at the point `P` is given by `(N)/(12) mu_(0)aJ`, then the value of `N` is

Answer

5

Explanation

`B_(1)=(mu_(0)Ja)/2-(mu_(0)Ja)/12`
`=((mu_(0)Ja)/2)(1-1/6)=5/6((mu_(0)Ja)/2)=(5mu_(0)Ja)/12=N/12mu_(0)aJ`
`=5`