Question

Which expression gives the vector form of the Biot–Savart law?

Options

• \[d\mathbf{B} = \frac{\mu_0}{4\pi}\frac{I\,d\mathbf{l} \times \mathbf{r}}{r^2}\]

• \[d\mathbf{B} = \frac{\mu_0}{4\pi}\frac{I\,d\mathbf{l} \times \mathbf{r}}{r^3}\]

• \[d\mathbf{B} = \frac{\mu_0}{4\pi}\frac{I\,\mathbf{r} \times d\mathbf{l}}{r^3}\]

• \[d\mathbf{B} = \frac{\mu_0}{4\pi}\frac{I\,d\mathbf{l} \cdot \mathbf{r}}{r^3}\]

Answer 1

The vector form is dB = (μ₀/4π)(I dl × r)/r³, where the cross product captures the fact that dB is perpendicular to the plane containing both dl and r. Note that r appears cubed in the denominator; reversing the cross product order would reverse the field direction.