# Energy stored in a magnetic field!

An infinite straight solid cylindrical wire contains a uniform current density of magnitude $$J$$ (the direction of the current is along the axis of the cylinder). Find the energy stored in the magnetic field (in S.I. units) within a cylindrical volume of radius $$R$$ and length $$L$$ whose axis is parallel to that of the wire and at a distance of $$d$$ from it.

$$\text{Details and Assumptions:}$$

$$\bullet$$Assume that the radius of the wire is sufficiently large so that the cylinder is entirely contained within it.

$$\bullet$$The magnetic energy density is given by $$\dfrac{\mathbf{B}\cdot\mathbf{B}}{2\mu_{0}}$$ where $$\mathbf{B}$$ is the magnetic field.

$$\bullet$$ $$J=\dfrac{10^{3}}{\pi}\text{A/m}^{2}$$

$$\bullet$$ $$R=2 \text{m}$$

$$\bullet$$ $$L=2 \text{m}$$

$$\bullet$$ $$d=2\sqrt{2} \text{m}$$

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