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A cylindrical cavity of diameter a exist...

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)Ja`, then the value of `N` is

Text Solution

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The correct Answer is:
`(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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  • Inside a long straight uniform wire of round cross-section, there is a long round cylindrical cavity whose axis is parallel to the axis of the wire and displaced from the latter by a distance l. A direct current of density j flows along the wire. Find the magnetic induction inside the cavity. Consider, in particular, the case l=0 .

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