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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