Question

A long straight wire carries a current along the $x-$axis. Consider the points $A(0,1,0),B(0,1,1),C(1,0,1)$ and $D(1,1,1)$. If the current is $i$ and the magnetic field at $D$ has magnitude $B,$ then,

• A. $B=\frac{{\mu }_{0}i}{2\sqrt{2}\pi }$
• B. $B=\frac{{\mu }_{0}i}{2\pi \sqrt{3}}$
• C. $B$ is parallel to the $z-$axis
• D. $B$ makes an angle of ${45}^o$ with the $xy$ plane

Answer 1

Answer: (A), (D)

The correct options are
A $B=\frac{{\mu }_{0}i}{2\sqrt{2}\pi }$
D $B$ makes an angle of ${45}^o$ with the $xy$ plane

Current around a long straight wire from Ampere's Law is given by-

$B\left(2\pi r\right)={\mu }_{0}i$

$⟹B=\frac{{\mu }_{0}i}{3\pi r}$

$r$ is the distance of the point from the axis of the wire=$\sqrt{1^2+1^2}=\sqrt{2}$

$⟹B=\frac{{\mu }_{0}i}{2\sqrt{2}\pi }$

The magnetic field is perpendicular to the vector pointing from axis to the point at which magnetic field is found.

The vector points from (1,0,0) to (1,1,1). Thus it makes angle ${45}^{\circ }C$ with the xy plane.