2. (30 points) A long cylindrical wire of radius R carries the uniform current density $\vec{j} = j_0 \hat{z}$. Integrate $\nabla \times \vec{A} = \mu_0 \vec{j}$ to find $\vec{A}$ in cylindrical coordinates and use it to calculate $\vec{B}$ for $\rho < R$ and $\rho > R$.
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The current density is given by j = joz, where jo is a constant and z is the axial coordinate. To find the current enclosed by a circular loop of radius r, we need to integrate the current density over the area of the loop. The area of the loop is given by A = Show more…
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