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Illustration B-field along the z-axis (graph) of a current-carrying ring

<span>B-field along the z-axis (graph) of a current-carrying ring</span>
B-field along the z-axis (graph) of a current-carrying ring
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Magnetic field vs. position graph of an annular current-carrying conductor loop oriented perpendicular to the z-axis, with the \(z\) axis passing through the center of the ring. The graph shows the shape of the magnetic field \(\class{violet}{\boldsymbol{B}}\) along the \(z\) axis.

Exactly in the center of the ring the magnetic field has a maximum. The magnetic field decreases along the z-axis in both directions as follows:$$ \class{violet}{\boldsymbol{B}}(z) ~=~ \frac{\mu_0 \, I }{ 2 } \, \frac{R^2}{ (R^2 ~+~ z^2)^{\frac{3}{2}} } $$where \(I\) is the current through the ring and \(R\) is the radius of the ring.