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# Magnetic Fields Surrounding a Current Carrying Wire

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A long wire with a solid metal core is surrounded by a layer of insulator. A cross section view of the wire is shown in the accompanying figure: The center of the wire is located at the origin. The solid portion of the wire, labeled region 1, has $r < r_a$, and the insulator portion of the wire, labeled region 2, has $r_1 < r < r_2$. The core carries a current which is uniformly distributed over the cross-section of the core according to $i(r)=i_o \,\ A/m^2$. The current is in the direction of a vector out of the plane of the drawing.

What is the magnetic field, magnitude and direction, in the region $r_1 < r < r_2$?

A

$B(r_1 < r < r_2 ) =\cfrac{\mu_o i_o r_1 ^2 }{2 \pi r^2}$
clockwise on the drawing.

B

$B(r_1 < r < r_2 ) =\cfrac{\mu_o i_o r_1 ^2 }{2 r}$
clockwise on the drawing.

C

$B(r_1 < r < r_2 ) =\cfrac{\mu_o i_o r_1 ^2 }{2 \pi r^2}$
counter clockwise on the drawing.

D

$B(r_1 < r < r_2 ) =\cfrac{\mu_o i_o r_1 ^2 }{2 r}$
counter clockwise on the drawing.