Question

The magnetic filed (dB) due to smaller element (dl) at a distance $\left(\overrightarrow{r}\right)$ from element carrying current i, is

• A. $dB=\frac{{\mu }_{0}i}{4\pi }\left(\frac{\overrightarrow{dl}\times \overrightarrow{r}}{r}\right)$
• B. $dB=\frac{{\mu }_{0}i}{4\pi }{i}^2\left(\frac{\overrightarrow{dl}\times \overrightarrow{r}}{r^2}\right)$
• C. $dB=\frac{{\mu }_{0}i}{4\pi }{i}^3\left(\frac{\overrightarrow{dl}\times \overrightarrow{r}}{2r^2}\right)$
• D. $dB=\frac{{\mu }_0}{4\pi }i\left(\frac{\overrightarrow{dl}\times \overrightarrow{r}}{r^3}\right)$

Answer 1

The correct option is D $dB=\frac{{\mu }_0}{4\pi }i\left(\frac{\overrightarrow{dl}\times \overrightarrow{r}}{r^3}\right)$

$dB=\frac{{\mu }_{0}i}{4\pi }\int \frac{(\overrightarrow{dl}\times \hat{r})}{r^2}$

we know that=$\hat{r}=\frac{\overrightarrow{r}}{r}$

$dB=\frac{{\mu }_{0}i}{4\pi }\int \frac{(\overrightarrow{dl}\times \overrightarrow{r})}{r^3}$