Question

A vertical wire kept in $xz$-plane carries a current from $\text{Q}$ to $\text{P}$ as shown in figure. The magnetic field due to current will have the direction at the origin $\text{O}$ along

• A. $OX$
• B. $O{X}^{{}^{\prime }}$
• C. $OY$
• D. $O{Y}^{{}^{\prime }}$

Answer 1

The correct option is D $O{Y}^{{}^{\prime }}$

Using, Biot-savart law(in vector form),

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

Direction of field is given by $(\overrightarrow{dl}\times \overrightarrow{r})$

Here, $(\overrightarrow{dl}\times \overrightarrow{r})=(\hat{k}\times -\hat{i})=-\hat{j}$

Hence, field at $\text{O}$ is directed along $\text{OY'}$

<!--td {border: 1px solid #ccc;}br {mso-data-placement:same-cell;}--> Hence, $\left(D\right)$ is the correct answer.