The electric current in a conductor:

$\overline{){{\mathbf{i}}}_{{\mathbf{r}}}{\mathbf{}}{\mathbf{=}}{\mathbf{}}{\mathbf{\left(}}{\mathbf{\pi}}{{\mathbf{r}}}^{{\mathbf{2}}}{\mathbf{\right)}}{\mathbf{J}}}$

Ampere's law:

$\overline{){\mathbf{\oint}}{\mathbf{B}}{\mathbf{\xb7}}{\mathbf{d}}{\mathbf{l}}{\mathbf{}}{\mathbf{=}}{\mathbf{}}{{\mathbf{\mu}}}_{{\mathbf{0}}}{{\mathbf{i}}}_{\mathbf{e}\mathbf{n}\mathbf{c}}}$

**(a)**

At r less than a, the current in the conductor is:

i_{r} = πr^{2}J

An electric current is flowing through a long cylindrical conductor with radius a = 0.15 m. The current density J= 5.5 A/m^{2} uniform in the cylinder. In this problem, we consider an imaginary cylinder with radius r around the axis AB

(a) When r is less than a, express the current inside the imaginary cylinder i_{r} in terms of r and J.

(b) Express the magnitude of the magnetic field B at r in terms of the current through the imaginary cylinder i_{r} and its radius.

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