Question

A long straight wire along Z-axis carries a current I in the positive Z-direction.The magnetic vector field $\overrightarrow{B}$ at a point having coordinate (x,y) in the Z=0 plane is:

• A. $\frac{{\mu }_{0}I(y\hat{i}-x\hat{j})}{2\pi (x^2+y^2)}$
• B. $\frac{{\mu }_{0}I(x\hat{i}+y\hat{j})}{2\pi (x^2+y^2)}$
• C. $\frac{{\mu }_{0}I(x\hat{j}-y\hat{i})}{2\pi (x^2+y^2)}$
• D. $\frac{{\mu }_{0}I(x\hat{i}-y\hat{j})}{2\pi (x^2+y^2)}$

Answer 1

The correct option is B $\frac{{\mu }_{0}I(x\hat{i}+y\hat{j})}{2\pi (x^2+y^2)}$

For a long straight wire,magnetic field is $\overrightarrow{B}=\frac{{\mu }_{0}I}{2\pi r}\hat{r}$ where $I$ is the current,$\hat{r}$ is the radial vector direction,$r$ is the distance

$\overrightarrow{B}=\frac{{\mu }_{0}Ir}{2\pi r^2}\hat{r}$ (multiplying and divinding by r)

$=\frac{{\mu }_{0}I\hat{r}}{2\pi r^2}=\frac{{\mu }_{0}I(x\hat{i}+y\hat{j})}{2\pi (x^2+y^2)}$