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

A cylindrical cavity of diameter a exists inside a cylinder of diamete

1.	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» Correct Answer - `(5)` (5) `B_1=(mu_Jpia^2)/(2pia)=(mu_0Ja)/2,B_2=(mu_Jpi(a//2)^2)/(2pi(3a//2))=(mu_0Ja)/12` `B_1-B_2=(mu_Ja)/2-(mu_Ja)/12` `=((mu_0Ja)/2)(1-1/6)=5/6((mu_0Ja)/2)=(5mu_0aJ)/12` `=N/12mu_0aJ` `:. N=5`

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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

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