Question

Current $I$ is flowing along the path $ABCD$, along the four edges of the cube (figure-a), produces a magnetic field $B_0$ at the centre of the cube. Find the magnetic field $B$ produced at the centre of the cube by a current $I$ flowing along the path of the six edges $ABCGHEA$ (figure-b) :

Answer 1

Current I is flowing along the path ABCD of the cube
$\therefore$ From the symmetry along the cube, we have the magnetic field as,

$\overrightarrow{B}=B_x\hat{i}+B_y(-\hat{j})+B_2\hat{k}$

As the magnetic field in different direction is $B_o$

$B=\sqrt{B_o^2+B_o^2+B_o^2}=\sqrt{3}{B}_o$ towards F