1. A steady current I flows down a long cylindrical wire of radius a. Find the magneticfreld, both inside and outside the wire, if (a) the current is uniformly distributed over theouter surface of the wire and (b) the current is distributed in such a way that J isproportional to the distance to the axis

Question
Asked Oct 22, 2019
1. A steady current I flows down a long cylindrical wire of radius a. Find the magnetic
freld, both inside and outside the wire, if (a) the current is uniformly distributed over the
outer surface of the wire and (b) the current is distributed in such a way that J is
proportional to the distance to the axis
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1. A steady current I flows down a long cylindrical wire of radius a. Find the magnetic freld, both inside and outside the wire, if (a) the current is uniformly distributed over the outer surface of the wire and (b) the current is distributed in such a way that J is proportional to the distance to the axis

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Expert Answer

Step 1

(a) Let the radius of amperian loop be r. For r < a, the magnetic field is zero. Outside the loop, the magnetic field is given by,

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Step 2

(b) Current density J is proportional to r. Therefore, the current is,

I-[JdA
S
(kr)(2rdr)
27Tka
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I-[JdA S (kr)(2rdr) 27Tka

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Step 3

For r < a, the curre...

Ic=Jd4
k) (2 Trdr)
27Tk
3
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Ic=Jd4 k) (2 Trdr) 27Tk 3

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