the question is that:(adsbygoogle = window.adsbygoogle || []).push({});

A long, straight, solid cylinder, oriented with its axis in the z-direction, carries a current whose current density is [itex] \vec J[/itex]. The current density, although symmetrical about the cylinder axis, is not constant but varies according to the relation

(the relation is in the attachment)

where a is the radius of the cylinder, r is the radial distance from the cylider axis, and [itex]I_0[/itex] is a constant haveing units of amperes.

a) show that [itex]I_0[/itex] is the total current passing through the entire cross section of the wire.

b). Using Ampere's law, derive an expression for the magnitude of the magnetic field [itex]\vec B[/itex] in the region r>=a .

c). Obtain an expression for the current I contained in a circular cross section of radius r<=a and centered at the cylinder axis.

d). Using Ampere's law, derive an expression for the magnitude of the magnetic field [itex]\vec B[/itex] in the region r<=a.

For a, Since for the entire cross section of the wire, i subt. r=a into the relation. But it will give zero. I shown nothing. If I subt. J=I/A,

then [itex]I=2 I_0 [1- (\frac{r}{a})^2][/itex]. Anything wrong,

and how to proof that?

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# Homework Help: Sources of Magnetic Field

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