Question

The magnetic field at the origin due to a current element \(\overrightarrow{idl}\) placed at a point with vector position \(\overrightarrow{r}\) is

• A. \(\frac{\mu_0 i}{4\pi} \frac{\vec{dl} \times \vec{r}} {{r^3}}\)
• B. \(\frac{\mu_0 i}{4\pi}\frac{\vec{r} \times \vec{dl}}{r^3}\)
• C. \(\frac{\mu_0 i}{4\pi} \frac{\vec{dl} \times \vec{r}} {{r^2}}\)
• D. \(\frac{\mu_0 i}{4\pi}\frac{\vec{r} \times \vec{dl}}{r^2}\)

Answer 1

The Correct Option is A

The magnetic field \(\vec{B}\) due to a current element \(i \, d\vec{l}\) at a point with position vector \(\vec{r}\) is given by the Biot-Savart law: \[ \vec{B} = \frac{\mu_0 i \, d\vec{l} \times \vec{r}}{4 \pi r^3} \] Where:
\(\mu_0\) is the permeability of free space,
\(i\) is the current,
\(d\vec{l}\) is the current element,
\(\vec{r}\) is the position vector,
\(r\) is the distance between the current element and the point where the magnetic field is being calculated.
Thus, the magnetic field at the origin due to the current element is given by option (A).

The correct option is (A):\(\frac{\mu_0 i}{4\pi} \frac{\vec{dl} \times \vec{r}} {{r^3}}\)