A cylinderical cavity of diameter a exists inside a cylinder of diameter 2a as shown in the figure. Both the cylinder and the cavity are infinitely 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_(R)=B_(T)-B_(C)` R= remaining portion T= total portion and C= cavity
`B_(R)=(mu_(0)I_(T))/(2Api) - (mu_(0)I_(C))/(2(3a//2)pi)`…….i , `I_(T)=J(pia^(2))I_(C)=J((pia^(2))/4)`
Substituting the value in eq (i) we have `B_(R)=(mu_(0))/(a pi)[(I_(T))/2-(T_(C))/3]=(mu_(0))/(a pi)[(pia^(2)J)/2- (pia^(2)J)/12]=(5mu_(0)aJ)/12:.N=5`