Question

Magnetic field due to a current element $\overrightarrow{dl}$ at point $\text{P}$ is zero. Then, it is possible that,

• A. Point $\text{P}$ is at an infinite distance from current element.
• B. Point $\text{P}$ lies on the axis of current element.
• C. Nothing can be said about point $\text{P}$ based on the information given.
• D. Both options $\left(a\right)$ and $\left(b\right)$

Answer 1

The correct option is D Both options $\left(a\right)$ and $\left(b\right)$

Applying Biot- Savart's law,

$\overrightarrow{dB}=\frac{{\mu }_0}{4\pi }\frac{i\overrightarrow{dl}\times \overrightarrow{r}}{r^3}$

Taking magnitude of magnetic field intensity only,

$dB=\frac{{\mu }_{0}i}{4\pi }\frac{dl\sin \theta }{r^2}$

From the above expression, we can easily observe that

$dB=0$, if $\theta =0^{\circ }\text{or}{180}^{\circ }$

i.e. when point $\text{P}$ lies on axis of current element. So, option $\left(b\right)$ is correct.

And, $\overrightarrow{dB}\approx 0$ when $r\to \infty$

$\therefore$ option $\left(a\right)$ is also correct.

Hence, option $\left(d\right)$ is correct.