Q. The magnetic field $d\overrightarrow{B}$ due to a small current element $d\overrightarrow{l}$ at a distance $\overrightarrow{r}$ and element carrying current $i$ is Or Vector form of Bio-savart’s law is
A) $d\overrightarrow{B} = \frac{\mu_{0}}{4\pi}i\left( \frac{d\overrightarrow{l} \times \overrightarrow{r}}{r} \right)$
B) $d\overrightarrow{B} = \frac{\mu_{0}}{4\pi}i^{2}\left( \frac{d\overrightarrow{l} \times \overrightarrow{r}}{r} \right)$
C) $d\overrightarrow{B} = \frac{\mu_{0}}{4\pi}i^{2}\left( \frac{d\overrightarrow{l} \times \overrightarrow{r}}{r^{2}} \right)$
D) $d\overrightarrow{B} = \frac{\mu_{0}}{4\pi}i\left( \frac{d\overrightarrow{l} \times \overrightarrow{r}}{r^{3}} \right)$
Explanation
(d) $dB = \frac{\mu_{0}}{4\pi} \bullet \frac{idl\sin\theta}{r^{2}} \Rightarrow d\overrightarrow{B} = \frac{\mu_{0}}{4\pi} \bullet \frac{i(d\overrightarrow{l} \times \overrightarrow{r})}{r^{3}}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.