Question

What is the direction of magnetic field at point $\text{O}$ due to current carrying wire $\text{PQ}$?

• A. out of the plane i.e. $+Z$ axis
• B. into the plane i.e. $-Z$ axis
• C. can't be determined with the given data
• D. in the plane i.e. $X-Y$ plane

Answer 1

The correct option is A out of the plane i.e. $+Z$ axis

Using Biot- Savart law, magnetic field due to current carrying element is given by

$\overrightarrow{dB}=\frac{{\mu }_{0}i}{4\pi }\frac{\overrightarrow{dl}\times \overrightarrow{r}}{r^3}$

Thus, direction of magnetic field $\overrightarrow{dB}$ due to current carrying wire depends on $\overrightarrow{dl}\times \overrightarrow{r}$, means $\overrightarrow{dB}$ will be perpendicular to both $\overrightarrow{dl}$ and $\overrightarrow{r}$.

By applying right-hand thumb rule for any current element on $\text{PQ}$, we can easily get the direction of magnetic field at point $O$ and that will be pointing out of the given $X-Y$ plane i.e. $+Z$ axis.

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