Question

The magnetic field $dB$ at a point $rmeters$ away from a current element $I\overrightarrow{dl}$ aligning at angle of $\theta$ with respect to the current element is :

• A. $\left(\frac{{\mu }_o}{4\pi }\right)\left(\frac{Idlsin\theta }{r}\right)$
• B. $\left(\frac{{\mu }_o}{4\pi }\right)\left(\frac{Idl}{r^2}\right)$
• C. $\left(\frac{{\mu }_o}{4\pi }\right)\left(\frac{Idlsin\theta }{r^2}\right)$
• D. $\left(\frac{{\mu }_o}{4\pi }\right)\left(\frac{Idl}{r}\right)$

Answer 1

Answer: (C)

$\left(\frac{{\mu }_o}{4\pi }\right)\left(\frac{Idlsin\theta }{r^2}\right)$

According to Biot-Savart Law, the magnetic field $\overrightarrow{dB}$ at a point $r$ meter away from $I\overrightarrow{dl}$ is
$\overrightarrow{dB}=\frac{{\mu }_0}{4\pi }\left(\frac{I\overrightarrow{dl}\times \overrightarrow{r}}{r^3}\right)$
$⟹dB=\frac{{\mu }_0}{4\pi }\left(\frac{Idl\sin \theta }{r^2}\right)$