Question

A n infinitely long wire carries current $i_0$ along +z axis. Find flux through the right angled isosceles triangular region co-planar with the wire as shown in figure.

Answer 1

B is at (x,y) in Z=0 plane. So, B is perpendicular to OP.

From the figure,

$\overrightarrow{B}=B\sin \theta \hat{i}-B\cos \theta \hat{j}$

$\because \sin \theta =\frac{y}{r},\cos \theta =\frac{x}{r}\&B=\frac{{\mu }_{0}I}{2\pi r}$

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