Question

The direction of the magnetic field ‘dB’ due to current element ‘dL’ at a distance ‘r’ is the direction of
A. $r \times dL$
B. $dL \times r$
C. $\left( {rdL} \right)r$
D. $dL$

Answer 1

In this question, we need to determine the direction of the magnetic field due to current carrying element, which is situated at a distance ‘r’. For this, we will follow the Biot-Savart’s law in detail for the direction of the vectors

Complete step by step answer:
Biot-Savart’s law states that the direction of the magnetic field will be in the direction which is perpendicular to the direction of the length of the wire and the distance of the wire from the point where we need to determine the magnetic field. In other words, the direction of the magnetic field will be in the direction of the cross-product vector of the length of the wire and the distance of the wire from the point where we need to determine the magnetic field.
Mathematically, $\overrightarrow {dB} = \overrightarrow {dL} \times r$ where, $\overrightarrow {dB}$ in the direction of the magnetic field, $\overrightarrow {dL}$ be the direction of the length of the wire and $r$ be the distance of the wire from the point where we need to determine the magnetic field.
Hence, we can say that the direction of the magnetic field ‘dB’ due to current element ‘dL’ at a distance ‘r’ is the direction of $dL \times r$.

So, the correct answer is “Option B”.

Note:
Here, it is worth noting that no conversation of the direction of the current has been made. If the direction of the current has been included then, we have to follow the right-hand screw rule to determine the direction of the magnetic field.