Biot-Savart law indicates that an electron moving with a velocity \(\vec{V}\) produces a magnetic field \(\vec{B}\) around it such that

According to the Biot-Savart law, the magnetic field \(\vec{B}\) produced by a charge \(q\) moving with velocity \(\vec{V}\) at a position vector \(\vec{r}\) is given by

\(\vec{B} = \dfrac{\mu_0}{4\pi} \dfrac{q(\vec{V} \times \vec{r})}{r^3}\)

The direction of the magnetic field \(\vec{B}\) is determined by the cross product \(\vec{V} \times \vec{r}\).

By the properties of the cross product, the resulting vector \(\vec{B}\) is always perpendicular to both the velocity vector \(\vec{V}\) and the position vector \(\vec{r}\).

Therefore, \(\vec{B}\) is perpendicular to \(\vec{V}\).

Answer: \(\vec{B}\) is perpendicular to \(\vec{V}\)