The magnetic field \(\vec{dB}\) in terms of the current density \(\vec{j}\) of a conducting wire is related as
1
\( \vec{dB}=\dfrac{\mu_0 i}{4\pi} \dfrac{\vec{dl}\times \vec{r}}{r^3}\)
2
\( \vec{dB}=\frac{\mu_0}{4\pi} \frac{i.\vec{dl} sin θ}{r^2}\)
3
\(\vec{dB} =\dfrac{\mu_0}{4\pi} \dfrac{\vec{j}\times \vec{r}}{r^3}dV\)
4
\( \vec{dB}=\frac{\mu_0}{4\pi} \frac{i\times\vec{j}}{r^2}\)