The magnetic field doverrightarrow{B} due to | vedclass

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(D) According to the Biot-Savart Law,the magnetic field $dB$ due to a current element $idl$ at a distance $r$ is given by the magnitude: $dB = \frac{\

Vedclass · Accepted Answer

$d\overrightarrow{B} = \frac{\mu_0}{4\pi} i \left( \frac{d\overrightarrow{l} 	imes \overrightarrow{r}}{r^3} ight)$

Vedclass · Answer

(D) According to the Biot-Savart Law,the magnetic field $dB$ due to a current element $idl$ at a distance $r$ is given by the magnitude: $dB = \frac{\mu_0}{4\pi} \frac{idl \sin 	heta}{r^2}$.In vector form,this is expressed as $d\overrightarrow{B} = \frac{\mu_0}{4\pi} \frac{i(d\overrightarrow{l} 	imes \widehat{r})}{r^2}$.Since the unit vector $\widehat{r} = \frac{\overrightarrow{r}}{r}$,we substitute this into the equation:$d\overrightarrow{B} = \frac{\mu_0}{4\pi} \frac{i(d\overrightarrow{l} 	imes \overrightarrow{r})}{r^2 \cdot r} = \frac{\mu_0}{4\pi} \frac{i(d\overrightarrow{l} 	imes \overrightarrow{r})}{r^3}$.Thus,option $D$ is correct.

The magnetic field $d\overrightarrow{B}$ due to a small current element $d\overrightarrow{l}$ at a distance $\overrightarrow{r}$ from an element carrying current $i$ is given by:

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