Question

For a current distributed through a volume (rather than a thin wire), the Biot–Savart law is rewritten using the current density j = I/A, where:

Options

• the distance r² is replaced by the volume element dV

• I dl is replaced by j² dV, giving \[dB = \frac{\mu_0}{4\pi}\frac{\mathbf{j}^2 \times \mathbf{r}}{r^3}\,dV\]

• I dl is replaced by j dV, giving \[dB = \frac{\mu_0}{4\pi}\frac{\mathbf{j} \times \mathbf{r}}{r^3}\,dV\]

• the current I is replaced by j/A, keeping dl unchanged

Answer 1

For volume currents, the identity I dl = j dV is used, where j = I/A is the current density. The law then reads dB = (μ₀/4π)(j × r/r³) dV, integrating the contributions of current throughout the volume.