group Small Group Activity
30 min.
Static Fields 2022 (5 years)
magnetic fields current Biot-Savart law vector field symmetry
Power Series Sequence (E&M)
Ring Cycle Sequence
Students work in groups of three to use the Biot-Savart law
\[\vec{B}(\vec{r}) =\frac{\mu_0}{4\pi}\int\frac{\vec{J}(\vec{r}^{\,\prime})\times \left(\vec{r}-\vec{r}^{\,\prime}\right)}{\vert \vec{r}-\vec{r}^{\,\prime}\vert^3} \, d\tau^{\prime}\]
to find an integral expression for the magnetic field, \(\vec{B}(\vec{r})\), due to a spinning ring of charge.
In an optional extension, students find a series expansion for \(\vec{B}(\vec{r})\) either on the axis or in the plane of the ring, for either small or large values of the relevant geometric variable.
Add an extra half hour or more to the time estimate for the optional extension.