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Find the current density as a funciton ...

Find the current density as a funciton of distance `r` from the axis of a radially symmetrical parallel stream of electrons if the magentic induction inside the strems varies as `B = br^(2)`, wheree `b and `alpha` are positive contans.

Text Solution

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The correct Answer is:
`(b(alpha+1))/(mu_0) r^(alpha-1)`
From Ampere's law `B_(phi)2pir=mu_0int_0^rj(r')2pir'dr'`
`j(r')=current density at a distance r'`.
Given `B_(phi)=br^(alpha).`
Subtituting in above, `br^(alpha+1)=mu_0intj(r')r'dr'.`
Differentiating, we obtain
`(alpha+1)br^(alpha)=mu_0j(r)r`
` implies j(r) =(b(alpha+1))/(mu_0) r^(alpha-1)`
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