What source quantity appears in the Biot-Savart law for a small current element?

State the Biot-Savart law for the magnetic field contribution from a current element.

A current element points upward. The field point is directly to its right. What is the direction of \(d\vec B\)?

For \(I=4.0\,\mathrm A\), \(dl=3.0\,\mathrm{mm}\), \(r=0.20\,\mathrm m\), and \(\theta=90^\circ\), estimate \(dB\).

Why does a current element produce no magnetic field contribution at a point lying exactly along the element direction?

Why must Biot-Savart contributions be added as vectors rather than as scalars?

A short element has \(I=2.0\,\mathrm A\), \(dl=5.0\,\mathrm{mm}\), \(r=0.10\,\mathrm m\), and \(\theta=30^\circ\). Find \(dB\).

At the centre of a circular current arc of radius \(R\), why is every current element's contribution perpendicular to the plane of the arc?

Use Biot-Savart to derive the magnetic field at the centre of a circular arc of radius \(R\), current \(I\), and angle \(\phi\) in radians.

A semicircular wire of radius \(0.050\,\mathrm m\) carries \(6.0\,\mathrm A\). Straight radial leads connect to the arc. Find the field at the centre due to the arc and explain why the radial leads contribute zero.