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A long cylidrical conductor of radius R ...

A long cylidrical conductor of radius `R` carries a current i as shown in figure. The current desity `J` is a function of radius according to `J=br`, where `b` is a constant. Find an expression for the magnetic field `B`

a. at a distasnce `r_1ltR` and
b.at a distance `r_2gtR,` measured from the axis.

Text Solution

Verified by Experts

The correct Answer is:
`B_(1) = (mu_(0)br_(1)^(2))/(3),B_(2)=(mu_(0)(bR)^(3))/(3r_(2))`
`ointoversetrarrB doversetrarrl = mu_(0) SigmaI`
`B_(1) 2pi r_(1) = mu_(0) underset(0)overset(r_(1))intjdA =mu_(0) underset(0)overset(r_(1))intbr2pirdr`
` =mu_(0) 2pib(r^(3)/(3))_(0)^(r1) implies B_(1) = (mu_(0)r__1^(2)b)/(3)`
`ointoversetrarrB doversetrarrl = mu_(0) SigmaI`
`B 2pi r_(2) = mu_(0) underset(0)overset(R)intJdA =mu_(0) underset(0)overset(R)intbr2pirdr`
`B_(2).2pir_(2) = mu_(0) 2pib((R^(3))/(3))implies B_(2) = (mu_(0)bR^(3))/(3r_(2))`
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