A circular loop is placed in a vertical plane containing the...

Let the East direction be along the $+x$-axis, the North direction be along the $+y$-axis, and the vertically upward direction be along the $+z$-axis.

The circular loop is placed in the North-South vertical plane, which corresponds to the $y$-$z$ plane. The axis of the loop lies along the East-West direction, which is the $x$-axis.

At the topmost point of the loop, the position vector with respect to the center is $\vec{r} = R\hat{k}$.

The current at this topmost point flows towards the North, so the current element vector is $d\vec{l} = dl\hat{j}$.

According to the Biot-Savart law, the direction of the magnetic field at the center of the loop is given by the direction of $d\vec{l} \times (-\vec{r})$.

Calculating the cross product:
$\hat{j} \times (-\hat{k}) = -(\hat{j} \times \hat{k}) = -\hat{i}$

The $-\hat{i}$ direction corresponds to the West. Thus, the magnetic dipole moment of the loop points towards the West.

For a circular current-carrying loop, the magnetic field along its entire central axis points in the same direction as the magnetic dipole moment.

Therefore, the magnetic field points towards the West at all points on the axis, including both point $A$ (to the East) and point $B$ (to the West).