A) \[d\,\mathbf{\vec{B}}=\frac{{{\mu }_{0}}}{4\pi }\frac{Id\mathbf{\vec{l}}\,\sin \,\phi }{{{r}^{2}}}\]
B) \[d\,\mathbf{\vec{B}}=\frac{{{\mu }_{0}}}{4\pi }\frac{Idl\times \,\mathbf{\hat{r}}}{{{r}^{2}}}\]
C) \[d\,\mathbf{\vec{B}}=\frac{{{\mu }_{0}}}{4\pi }\frac{Id\mathbf{\vec{l}}\times \,\mathbf{\hat{r}}}{{{r}^{3}}}\]
D) \[d\,\mathbf{\vec{B}}=\frac{{{\mu }_{0}}}{4\pi }\frac{Id\mathbf{\vec{l}}\times \,\mathbf{\hat{r}}}{{{r}^{2}}}\]
Correct Answer: D
Solution :
Biot- Savart's law, \[dB=\frac{{{\mu }_{0}}}{4\pi }\frac{I\,dl\,\,\sin \theta }{{{r}^{2}}}\] In vector form, \[d\vec{B}=\frac{{{\mu }_{0}}}{4\pi }\frac{Id\,\vec{I}\times \hat{r}}{{{r}^{2}}}\]
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