A) \[d\,\mathbf{\vec{B}}=ki\frac{d\mathbf{\vec{l}}\times \mathbf{\hat{r}}}{{{r}^{3}}}\]
B) \[d\,\mathbf{\vec{B}}=k{{i}^{2}}\frac{d\mathbf{\vec{l}}\times \mathbf{\hat{r}}}{{{r}^{3}}}\]
C) \[d\,\mathbf{\vec{B}}=ki\frac{d\mathbf{\vec{l}}\times \mathbf{\vec{r}}}{{{r}^{3}}}\]
D) \[d\,\mathbf{\vec{B}}=ki\frac{\mathbf{\vec{r}}\times d\,\mathbf{\vec{l}}}{{{r}^{2}}}\]
Correct Answer: C
Solution :
According to Biot-Savart's law\[dB=\frac{k\,I\,d\,l\,\sin \,\theta }{{{r}^{2}}}\,\hat{r}\] or \[d\vec{B}=\frac{kI\,d\,\vec{I}\,\times \vec{r}}{{{r}^{3}}}\]
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