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The current density vecj inside a long, ...

The current density `vecj` inside a long, solid, cylindrica wire of radius `a=12mm` is in the direction of the central axix, and its magnitude varies linearly with raidal distance `r` from the axis according to `J=(J_(0)r)/(a)`, where `J_(0)=(10^(5))/(4pi) A//m^(2)`. Find the magnitude of the magnetic field at `r=(9)/(a)` in `muT`.

Text Solution

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The correct Answer is:
10

Current in the element `= G(2 pi r.dr)`
Current encloded by Amperian loop of radius
`(a)/(2)=underset(0)overset(a//3)(int) (J_(0)r)/(a).2pir.dr=(2 piJ_(0))/(3a)((a)/(2))^(3)=(pi J_(0)a^(2))/(12)`
Applying Ampere's law
`B.2pi .(a)/(2)=mu_(0).(po J_(0)a^(2))/(12) rArr B =(mu_(0)J_(0)a)/(12)`
On putting values
`B =10 mu T`.
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