# A long straight wire along the z-axis carries a current I in the negative z direction. The magnetic vector field $\vec{B}$  at a point having coordinates (x, y) in the z = 0 plane is Option 1) $\frac{\mu 0I\left (yi^{\wedge }-xj^{\wedge }\right )}{2\pi\left ( x^{2}+y^{2} \right )}$   Option 2) $\frac{\mu 0I\left (xi^{\wedge }-yj^{\wedge }\right )}{2\pi\left ( x^{2}+y^{2} \right )}$ Option 3) $\frac{\mu 0I\left (xj^{\wedge }-yi^{\wedge }\right )}{2\pi\left ( x^{2}+y^{2} \right )}$ Option 4) $\frac{\mu 0I\left (xi^{\wedge }-yj^{\wedge }\right )}{2\pi\left ( x^{2}+y^{2} \right )}$

As we learnt in

For Infinite Length -

$\phi_{1}=\phi_{2}=90^{\circ}$

$B=\frac{\mu_{o}}{4\pi}\:\frac{2i}{r}\:$

- wherein

Magnitude of magnetic field $=\frac{\mu _oI}{2 \pi r}=\frac{\mu _oI}{2 \pi (x^{2}+y^{2})^{1/2}}$

Direction of field along tangential direction$=\frac{y\hat{i}{-x\hat{j}}}{\sqrt{x^{2}+y^{2}}}$

$\therefore \vec{B}=\frac{\mu_oI}{2\pi (x^{2}+y^{2})}.(y\hat{i}{ -x\hat{j}})$

Option 1)

$\frac{\mu 0I\left (yi^{\wedge }-xj^{\wedge }\right )}{2\pi\left ( x^{2}+y^{2} \right )}$

correct

Option 2)

$\frac{\mu 0I\left (xi^{\wedge }-yj^{\wedge }\right )}{2\pi\left ( x^{2}+y^{2} \right )}$

incorrect

Option 3)

$\frac{\mu 0I\left (xj^{\wedge }-yi^{\wedge }\right )}{2\pi\left ( x^{2}+y^{2} \right )}$

incorrect

Option 4)

$\frac{\mu 0I\left (xi^{\wedge }-yj^{\wedge }\right )}{2\pi\left ( x^{2}+y^{2} \right )}$

incorrect

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