PROBLEM $6(20$pts$)$

A hollow conducting pipe of inner radius $\backslash ($ a $\backslash )$ and outer radius $\backslash ($ b $\backslash )$ carries a current $\backslash ($ I $\backslash )$ parallel to its axis and distributed uniformly through the pipe material.

Find expressions for the magnetic field for

a$)(7$pts$)\backslash (\backslash$mathrm$\{$r$\}$b $\backslash ),$ where r is the radial distance from the pipe axis.

Problem $3(15$pts$)$:

A current of uniform linear density $\backslash (\backslash$mathrm$\{$J$\}\_\{5\}\backslash )$ passes through a thin infinite sheet, as shown in the figure below. An infinite long wire is placed at a distance $\backslash ($ h $\backslash )$ from the sheet. A current if flows through the wire.

Find:

a$)(5$pts$)$ The magnetic field generated by the infinite sheet

b$)(5$pts$)$ The force per unit length exerted on the wire

c$)(5$pts$)$ The distance $\backslash ($ y $\backslash )$ above the infinite sheet where the total magnetic field is zero