Question

Current $I$ flows around the wire frame along the edges of a cube as shown in figure. Point $P$ is the center of the cube. The incoming and outgoing wires have orientation toward $P$. Then

• A. the magnetic field at $P$ is toward $+y$ direction
• B. the magnetic field at $P$ is toward $-y$ direction
• C. the unit vector of magnetic field at $P$ is $-\frac{1}{\sqrt{2}}(\hat{i}-\hat{j})$
• D. the magnitude of magnetic field at $P$ is $\frac{{4\sqrt{2}\mu }_{0}i}{3\pi a}$

Answer 1

Answer: (A)

the magnetic field at $P$ is toward $+y$ direction

Let us suppose $2$ current carrying conductors are place between AF as well as between FB
The current in those conductors/wire are equal opposite. So there is no current in any direction along those points
Now (figure $2$)
So magnetic field due to current carrying loop AEHD at point P=$=\left(B_0\right)\left(\widehat{-k}\right)$ (By right hand screw rule)
Net magnetic field at Point P$=B_0\left(\widehat{-k}\right)+B_0\hat{j}+B_0\left(\widehat{+k}\right)$
$=B_0\hat{j}$
Direction of magnetic field at point P is in the $+y$ direction
So answer is A